Atkin-Lehner |
3+ 5+ 31- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
99975b |
Isogeny class |
Conductor |
99975 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
479232 |
Modular degree for the optimal curve |
Δ |
10895712890625 = 33 · 510 · 312 · 43 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 2 0 -2 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-378188,89360156] |
[a1,a2,a3,a4,a6] |
Generators |
[275:2362:1] [380:647:1] |
Generators of the group modulo torsion |
j |
382848536477869561/697325625 |
j-invariant |
L |
6.7798108437416 |
L(r)(E,1)/r! |
Ω |
0.61659440289315 |
Real period |
R |
5.4977881830731 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999996927 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
19995i1 |
Quadratic twists by: 5 |