Atkin-Lehner |
2+ 3+ 5- 11+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
58410b |
Isogeny class |
Conductor |
58410 |
Conductor |
∏ cp |
88 |
Product of Tamagawa factors cp |
deg |
895488 |
Modular degree for the optimal curve |
Δ |
-72884728125000000 = -1 · 26 · 33 · 511 · 114 · 59 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -3 11+ -3 -1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-511089,141361245] |
[a1,a2,a3,a4,a6] |
Generators |
[346:2247:1] [-174:15087:1] |
Generators of the group modulo torsion |
j |
-546827097630239553483/2699434375000000 |
j-invariant |
L |
7.3456027121156 |
L(r)(E,1)/r! |
Ω |
0.3472382607008 |
Real period |
R |
0.24039043947454 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999977 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
58410u1 |
Quadratic twists by: -3 |