Atkin-Lehner |
3+ 5+ 13- 53- |
Signs for the Atkin-Lehner involutions |
Class |
31005d |
Isogeny class |
Conductor |
31005 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
250560 |
Modular degree for the optimal curve |
Δ |
-60631946169721875 = -1 · 33 · 55 · 136 · 533 |
Discriminant |
Eigenvalues |
0 3+ 5+ -4 -6 13- -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,64692,-10012101] |
[a1,a2,a3,a4,a6] |
Generators |
[137:1192:1] |
Generators of the group modulo torsion |
j |
1108949275696693248/2245627635915625 |
j-invariant |
L |
1.9320413194521 |
L(r)(E,1)/r! |
Ω |
0.18279155870097 |
Real period |
R |
2.6424104772431 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
31005g2 |
Quadratic twists by: -3 |