Atkin-Lehner |
2+ 3- 5- 11- 31- |
Signs for the Atkin-Lehner involutions |
Class |
30690q |
Isogeny class |
Conductor |
30690 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
294912 |
Modular degree for the optimal curve |
Δ |
275279309653708800 = 212 · 37 · 52 · 113 · 314 |
Discriminant |
Eigenvalues |
2+ 3- 5- 0 11- -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-203229,24674053] |
[a1,a2,a3,a4,a6] |
Generators |
[-223:7784:1] |
Generators of the group modulo torsion |
j |
1273369450418524369/377612221747200 |
j-invariant |
L |
4.4106419401848 |
L(r)(E,1)/r! |
Ω |
0.28708236121626 |
Real period |
R |
0.32007669633395 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10230w1 |
Quadratic twists by: -3 |