Cremona's table of elliptic curves

Curve 68355n1

68355 = 32 · 5 · 72 · 31



Data for elliptic curve 68355n1

Field Data Notes
Atkin-Lehner 3- 5+ 7- 31+ Signs for the Atkin-Lehner involutions
Class 68355n Isogeny class
Conductor 68355 Conductor
∏ cp 32 Product of Tamagawa factors cp
deg 2211840 Modular degree for the optimal curve
Δ 1.2116205971562E+19 Discriminant
Eigenvalues  1 3- 5+ 7- -4  6 -2 -4 Hecke eigenvalues for primes up to 20
Equation [1,-1,0,-2549430,-1557183825] [a1,a2,a3,a4,a6]
Generators [22570:3370695:1] Generators of the group modulo torsion
j 21366693269481169/141270303825 j-invariant
L 5.5979184105537 L(r)(E,1)/r!
Ω 0.11952583462636 Real period
R 5.8542975552504 Regulator
r 1 Rank of the group of rational points
S 0.999999999824 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 22785q1 9765l1 Quadratic twists by: -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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