Cremona's table of elliptic curves

Curve 71175d1

71175 = 3 · 52 · 13 · 73



Data for elliptic curve 71175d1

Field Data Notes
Atkin-Lehner 3+ 5+ 13+ 73- Signs for the Atkin-Lehner involutions
Class 71175d Isogeny class
Conductor 71175 Conductor
∏ cp 16 Product of Tamagawa factors cp
deg 614400 Modular degree for the optimal curve
Δ -7008597134296875 = -1 · 35 · 57 · 13 · 734 Discriminant
Eigenvalues -2 3+ 5+ -1  3 13+ -5  6 Hecke eigenvalues for primes up to 20
Equation [0,-1,1,-27758,4412918] [a1,a2,a3,a4,a6]
Generators [-218:237:1] [61:1715:1] Generators of the group modulo torsion
j -151385348878336/448550216595 j-invariant
L 4.8777262602542 L(r)(E,1)/r!
Ω 0.36945295511408 Real period
R 0.82516024583247 Regulator
r 2 Rank of the group of rational points
S 1.0000000000014 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 14235j1 Quadratic twists by: 5


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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