Cremona's table of elliptic curves

Curve 68241k1

68241 = 3 · 232 · 43



Data for elliptic curve 68241k1

Field Data Notes
Atkin-Lehner 3- 23- 43- Signs for the Atkin-Lehner involutions
Class 68241k Isogeny class
Conductor 68241 Conductor
∏ cp 12 Product of Tamagawa factors cp
deg 684288 Modular degree for the optimal curve
Δ -18678814520209401 = -1 · 3 · 238 · 433 Discriminant
Eigenvalues  1 3- -3 -1  5  3 -4 -5 Hecke eigenvalues for primes up to 20
Equation [1,0,1,-148925,-23089675] [a1,a2,a3,a4,a6]
j -2467489596697/126177609 j-invariant
L 1.4538443556716 L(r)(E,1)/r!
Ω 0.12115369589364 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 2967b1 Quadratic twists by: -23


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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