Atkin-Lehner |
2+ 3- 11+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
120384be |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
307200 |
Modular degree for the optimal curve |
Δ |
-17122002518016 = -1 · 214 · 36 · 11 · 194 |
Discriminant |
Eigenvalues |
2+ 3- -3 2 11+ -4 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-22224,1290656] |
[a1,a2,a3,a4,a6] |
Generators |
[89:133:1] |
Generators of the group modulo torsion |
j |
-101634915328/1433531 |
j-invariant |
L |
5.4337891967106 |
L(r)(E,1)/r! |
Ω |
0.69513384141153 |
Real period |
R |
1.9542240578834 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000016815 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
120384dm1 15048h1 13376k1 |
Quadratic twists by: -4 8 -3 |