Cremona's table of elliptic curves

Curve 12408c1

12408 = 23 · 3 · 11 · 47



Data for elliptic curve 12408c1

Field Data Notes
Atkin-Lehner 2- 3+ 11+ 47- Signs for the Atkin-Lehner involutions
Class 12408c Isogeny class
Conductor 12408 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 3072 Modular degree for the optimal curve
Δ 33030096 = 24 · 3 · 114 · 47 Discriminant
Eigenvalues 2- 3+  2  0 11+ -6  6  4 Hecke eigenvalues for primes up to 20
Equation [0,-1,0,-87,-120] [a1,a2,a3,a4,a6]
Generators [17:55:1] Generators of the group modulo torsion
j 4604090368/2064381 j-invariant
L 4.4254510905075 L(r)(E,1)/r!
Ω 1.6285154571836 Real period
R 2.7174756438364 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 24816f1 99264y1 37224f1 Quadratic twists by: -4 8 -3


Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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