Cremona's table of elliptic curves

Curve 12558c1

12558 = 2 · 3 · 7 · 13 · 23



Data for elliptic curve 12558c1

Field Data Notes
Atkin-Lehner 2+ 3+ 7+ 13- 23- Signs for the Atkin-Lehner involutions
Class 12558c Isogeny class
Conductor 12558 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 41472 Modular degree for the optimal curve
Δ 6636680773632 = 224 · 33 · 72 · 13 · 23 Discriminant
Eigenvalues 2+ 3+ -2 7+ -4 13-  6 -4 Hecke eigenvalues for primes up to 20
Equation [1,1,0,-9606,-344556] [a1,a2,a3,a4,a6]
Generators [-59:175:1] Generators of the group modulo torsion
j 98044243279969897/6636680773632 j-invariant
L 2.0015416857334 L(r)(E,1)/r!
Ω 0.48428691626309 Real period
R 4.1329666743382 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 100464ce1 37674s1 87906q1 Quadratic twists by: -4 -3 -7


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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