Atkin-Lehner |
2- 3+ 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
30324b |
Isogeny class |
Conductor |
30324 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-1957321673349168 = -1 · 24 · 3 · 74 · 198 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ -2 -2 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-111669,14557218] |
[a1,a2,a3,a4,a6] |
Generators |
[11396:34295:64] |
Generators of the group modulo torsion |
j |
-204589760512/2600283 |
j-invariant |
L |
3.1261377842467 |
L(r)(E,1)/r! |
Ω |
0.46861248010869 |
Real period |
R |
3.3355255322283 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
121296di1 90972c1 1596d1 |
Quadratic twists by: -4 -3 -19 |