Cremona's table of elliptic curves

Curve 65728b1

65728 = 26 · 13 · 79



Data for elliptic curve 65728b1

Field Data Notes
Atkin-Lehner 2+ 13+ 79+ Signs for the Atkin-Lehner involutions
Class 65728b Isogeny class
Conductor 65728 Conductor
∏ cp 8 Product of Tamagawa factors cp
deg 36864 Modular degree for the optimal curve
Δ -10634264576 = -1 · 217 · 13 · 792 Discriminant
Eigenvalues 2+  1 -3 -1  0 13+  3 -6 Hecke eigenvalues for primes up to 20
Equation [0,1,0,543,1151] [a1,a2,a3,a4,a6]
Generators [115:1264:1] Generators of the group modulo torsion
j 134838286/81133 j-invariant
L 4.7624210127701 L(r)(E,1)/r!
Ω 0.78613439657313 Real period
R 0.75725299548745 Regulator
r 1 Rank of the group of rational points
S 0.99999999989173 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 65728q1 8216a1 Quadratic twists by: -4 8


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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