Cremona's table of elliptic curves

Curve 75712cp1

75712 = 26 · 7 · 132



Data for elliptic curve 75712cp1

Field Data Notes
Atkin-Lehner 2- 7- 13+ Signs for the Atkin-Lehner involutions
Class 75712cp Isogeny class
Conductor 75712 Conductor
∏ cp 4 Product of Tamagawa factors cp
deg 27648 Modular degree for the optimal curve
Δ -620232704 = -1 · 219 · 7 · 132 Discriminant
Eigenvalues 2-  1  3 7-  0 13+  6  4 Hecke eigenvalues for primes up to 20
Equation [0,1,0,191,703] [a1,a2,a3,a4,a6]
Generators [111:1184:1] Generators of the group modulo torsion
j 17303/14 j-invariant
L 10.58500125356 L(r)(E,1)/r!
Ω 1.0482676974321 Real period
R 2.5244031850792 Regulator
r 1 Rank of the group of rational points
S 0.99999999968893 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 75712g1 18928y1 75712by1 Quadratic twists by: -4 8 13


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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