Atkin-Lehner |
2+ 19+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
42598a |
Isogeny class |
Conductor |
42598 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
135360 |
Modular degree for the optimal curve |
Δ |
5770012921856 = 212 · 193 · 593 |
Discriminant |
Eigenvalues |
2+ 0 2 0 -2 -6 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-81701,-8967403] |
[a1,a2,a3,a4,a6] |
Generators |
[-23841664350:7976755471:144703125] |
Generators of the group modulo torsion |
j |
8793221558212827/841232384 |
j-invariant |
L |
3.952789888361 |
L(r)(E,1)/r! |
Ω |
0.28238716638168 |
Real period |
R |
13.99776745878 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000016 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42598e1 |
Quadratic twists by: -19 |