Atkin-Lehner |
2+ 3+ 7+ 19+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
42294b |
Isogeny class |
Conductor |
42294 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
760320 |
Modular degree for the optimal curve |
Δ |
-59147930789696448 = -1 · 26 · 32 · 710 · 193 · 53 |
Discriminant |
Eigenvalues |
2+ 3+ -4 7+ -4 2 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-126882,-21018060] |
[a1,a2,a3,a4,a6] |
Generators |
[636:12174:1] |
Generators of the group modulo torsion |
j |
-225906697793311715881/59147930789696448 |
j-invariant |
L |
1.2868353111261 |
L(r)(E,1)/r! |
Ω |
0.12476957248938 |
Real period |
R |
5.1568474807242 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
126882bh1 |
Quadratic twists by: -3 |