Atkin-Lehner |
2+ 3+ 13+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
31434d |
Isogeny class |
Conductor |
31434 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
68544 |
Modular degree for the optimal curve |
Δ |
-105041017458 = -1 · 2 · 33 · 137 · 31 |
Discriminant |
Eigenvalues |
2+ 3+ -4 -3 4 13+ -3 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1862,33870] |
[a1,a2,a3,a4,a6] |
Generators |
[31:69:1] |
Generators of the group modulo torsion |
j |
-148035889/21762 |
j-invariant |
L |
1.5477755270547 |
L(r)(E,1)/r! |
Ω |
1.0240136613311 |
Real period |
R |
0.37786984331901 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999991 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
94302cd1 2418c1 |
Quadratic twists by: -3 13 |