Cremona's table of elliptic curves

Curve 12985a1

12985 = 5 · 72 · 53



Data for elliptic curve 12985a1

Field Data Notes
Atkin-Lehner 5+ 7+ 53- Signs for the Atkin-Lehner involutions
Class 12985a Isogeny class
Conductor 12985 Conductor
∏ cp 6 Product of Tamagawa factors cp
deg 6624 Modular degree for the optimal curve
Δ -33722045 = -1 · 5 · 74 · 532 Discriminant
Eigenvalues  1  3 5+ 7+ -2 -4  2 -8 Hecke eigenvalues for primes up to 20
Equation [1,-1,0,-205,-1114] [a1,a2,a3,a4,a6]
j -397909449/14045 j-invariant
L 3.7764454322953 L(r)(E,1)/r!
Ω 0.62940757204922 Real period
R 1 Regulator
r 0 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 116865z1 64925a1 12985d1 Quadratic twists by: -3 5 -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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