Atkin-Lehner |
3+ 11+ 73+ |
Signs for the Atkin-Lehner involutions |
Class |
2409a |
Isogeny class |
Conductor |
2409 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
672 |
Modular degree for the optimal curve |
Δ |
-28857411 = -1 · 33 · 114 · 73 |
Discriminant |
Eigenvalues |
2 3+ 1 -2 11+ 2 -1 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-60,335] |
[a1,a2,a3,a4,a6] |
Generators |
[58:117:8] |
Generators of the group modulo torsion |
j |
-24288219136/28857411 |
j-invariant |
L |
5.0905813012467 |
L(r)(E,1)/r! |
Ω |
1.8999897469805 |
Real period |
R |
1.3396338873241 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
38544p1 7227g1 60225t1 118041i1 |
Quadratic twists by: -4 -3 5 -7 |