Atkin-Lehner |
2+ 3+ 17+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
7242d |
Isogeny class |
Conductor |
7242 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
698880 |
Modular degree for the optimal curve |
Δ |
141878319095808 = 213 · 315 · 17 · 71 |
Discriminant |
Eigenvalues |
2+ 3+ 4 -3 5 -5 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-33297588,-73968830640] |
[a1,a2,a3,a4,a6] |
Generators |
[-35229059386600986318651459600096005:17620204291549406520732240997175135:10573022565037191796411365018611] |
Generators of the group modulo torsion |
j |
4082837157516340847666290249/141878319095808 |
j-invariant |
L |
3.1721223347425 |
L(r)(E,1)/r! |
Ω |
0.062848708716405 |
Real period |
R |
50.47235495412 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
57936w1 21726bd1 123114k1 |
Quadratic twists by: -4 -3 17 |