Atkin-Lehner |
3- 5- 7+ 13- 17- |
Signs for the Atkin-Lehner involutions |
Class |
69615u |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
30 |
Product of Tamagawa factors cp |
deg |
244800 |
Modular degree for the optimal curve |
Δ |
-1471748336296875 = -1 · 36 · 56 · 7 · 13 · 175 |
Discriminant |
Eigenvalues |
-1 3- 5- 7+ 5 13- 17- 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,24223,-1146724] |
[a1,a2,a3,a4,a6] |
Generators |
[76:1024:1] |
Generators of the group modulo torsion |
j |
2156238418114871/2018859171875 |
j-invariant |
L |
4.6845886816215 |
L(r)(E,1)/r! |
Ω |
0.26155082427849 |
Real period |
R |
0.59702719923546 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999985487 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7735b1 |
Quadratic twists by: -3 |