Atkin-Lehner |
2+ 3- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122304cr |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
112 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
-106909388243094528 = -1 · 210 · 37 · 710 · 132 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- 2 13+ 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,101267,9709811] |
[a1,a2,a3,a4,a6] |
Generators |
[254:7203:1] |
Generators of the group modulo torsion |
j |
953312000000/887416803 |
j-invariant |
L |
8.7142931892539 |
L(r)(E,1)/r! |
Ω |
0.21900111855877 |
Real period |
R |
1.4211103486253 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000026176 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
122304eu1 15288w1 17472b1 |
Quadratic twists by: -4 8 -7 |