Atkin-Lehner |
2- 3+ 5+ 17+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
31620c |
Isogeny class |
Conductor |
31620 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
136800 |
Modular degree for the optimal curve |
Δ |
-204672386550000 = -1 · 24 · 3 · 55 · 175 · 312 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -1 5 -6 17+ -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-18206,-1163475] |
[a1,a2,a3,a4,a6] |
Generators |
[314157:33883651:27] |
Generators of the group modulo torsion |
j |
-41712978242216704/12792024159375 |
j-invariant |
L |
3.985245324074 |
L(r)(E,1)/r! |
Ω |
0.20231847083838 |
Real period |
R |
9.8489408988702 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
126480bi1 94860t1 |
Quadratic twists by: -4 -3 |