William A. Stein
September, 1998
Let p and be distinct primes. The modular curve X0(p) is ordinary at iff the Hecke operator T is invertible modulo . The following is a table which enumerates, for each prime p between 23 and 997, the set of primes for which the modular curve X0(p) is not ordinary.1
p | non-ordinary |
23 | 43 |
29 | - |
31 | - |
37 | 2, 3, 5, 17, 19 |
41 | - |
43 | 2, 7, 17, 37 |
47 | - |
53 | 3, 5, 11, 17 |
59 | 2, |
61 | 31, 101 |
67 | 2, 41, 71, 97 |
71 | 3, 5, 37 |
73 | 3, 43, 59, 71, 79 |
79 | - |
83 | 2, 5, 47, 73, 89 |
89 | 7, 29, 41, 101 |
97 | 7, 23 |
101 | 2, 7 |
103 | - |
107 | 2 |
109 | 3, 13, 79 |
113 | 7, 11 |
127 | 3, 37 |
131 | 2, 11, 29 |
137 | 7, 29 |
139 | 2, 7, 13, 19, 53 |
149 | 3, 13 |
151 | 5, 13, 37, 41, 83 |
157 | 5 |
163 | 2, 3, 17 |
167 | 11 |
173 | - |
179 | 2, 3, 17, 53, 71 |
181 | 29 |
191 | 13, 17, 71 |
193 | 5 |
197 | 2, 3, 5, 17, 59 |
199 | 7, 11, 53, 83 |
211 | 2, 29, 67 |
223 | - |
227 | 2, 7, 19, 89 |
229 | 7, 17, 37 |
233 | 23 |
239 | 29, 97 |
241 | 101 |
251 | 2 |
257 | 23 |
263 | 13, 19 |
269 | 2, 3, 73 |
271 | 5, 7 |
277 | 5, 23 |
281 | 13, 19, 59 |
283 | 2 |
293 | 3 |
307 | 2, 3, 5, 7, 13, 23, 29 |
311 | - |
313 | 19, 31 |
317 | 5, 11 |
331 | 2, 11, 41 |
337 | 5, 61 |
347 | 2, 5, 41, 61, 101 |
349 | 2 |
353 | 2, 5, 13, 19, 37 |
359 | 3, 5, 13, 23, 43, 47, 53, 97 |
367 | 5, 13 |
373 | 2, 7 |
379 | 2 |
383 | 13 |
389 | 2, 5, 7, 31, 79 |
397 | 3, 5, 7 |
401 | 2 |
409 | 2, 83 |
419 | 2 |
421 | 13, 41 |
431 | 3, 11 |
433 | 89 |
439 | 3, 31 |
443 | 2, 5, 13, 29 |
449 | 7 |
457 | 7, 61 |
461 | 5, 17, 31 |
463 | 5 |
467 | 2, 3 |
479 | 17 |
487 | 2, 3, 43, 67 |
491 | 2 |
499 | 2, 5, 19 |
503 | 3, 5, 7, 17, 29, 37, 71, 89, 101 |
509 | 5, 13 |
521 | 3, 5 |
523 | 2, 5, 7, 11, 41, 43 |
541 | - |
547 | 2, 7, 17, 23 |
557 | 2, 5, 23, 31, 43, 89 |
563 | 2, 97 |
569 | 7, 71 |
571 | 2, 17, 19, 23, 37, 41, 43, 47, 79, 83 |
577 | 2, 3, 5, 23, 29, 47 |
587 | 2, 11, 19, 43 |
593 | 3, 23, 31, 59, 83 |
599 | 19 |
601 | - |
607 | 31, 59 |
613 | 79 |
617 | 23 |
619 | 2, 5, 7, 41 |
631 | 5, 101 |
641 | 17, 59 |
643 | 2, 7, 13, 43, 67 |
647 | 3, 29, 61, 79 |
653 | 83 |
659 | 2, 3, 7, 11, 19, 23, 29, 79, 83 |
661 | 3 |
673 | 29, 43 |
677 | 2, 5, 43, 59, 101 |
683 | 2 |
691 | 2, 5, 47, 73 |
701 | 2, 11, 79 |
709 | 2, 41, 61, 67 |
719 | 7, 11 |
727 | - |
733 | 5, 7, 11, 29, 89, 101 |
739 | 2, 3, 5 |
743 | 5, 13 |
751 | 2, 29 |
757 | 2, 3 |
761 | 2 |
769 | 7 |
773 | 2, 3, 5, 19, 37, 53 |
787 | 2, 79 |
797 | 5, 7, 47, 53, 61 |
809 | 2, 47 |
811 | 3, 7, 11 |
821 | 3, 11, 79 |
823 | 43 |
827 | 2, 3, 5, 7, 13, 23, 41, 59 |
829 | 2, 3, 11, 19, 31 |
839 | 3, 5 |
853 | 29, 43 |
857 | 17, 23 |
859 | 2, 5, 43 |
863 | 3, 7, 11, 19, 47 |
877 | 2 |
881 | 7 |
883 | 2, 3, 59 |
887 | 2 |
907 | 2 |
911 | 11 |
919 | 2, 5, 13 |
929 | 5, 11, 13 |
937 | - |
941 | 5, 79 |
947 | 2 |
953 | 3, 5 |
967 | - |
971 | 2 |
977 | 7 |
983 | 7, 11 |
991 | 83 |
997 | 2, 5, 11, 13, 29, 31, 41, 79, 83, 97 |