Cremona's table of elliptic curves

Curve 56355r1

56355 = 3 · 5 · 13 · 172



Data for elliptic curve 56355r1

Field Data Notes
Atkin-Lehner 3- 5+ 13- 17+ Signs for the Atkin-Lehner involutions
Class 56355r Isogeny class
Conductor 56355 Conductor
∏ cp 48 Product of Tamagawa factors cp
deg 4386816 Modular degree for the optimal curve
Δ 8.0493894782804E+22 Discriminant
Eigenvalues -1 3- 5+ -2  2 13- 17+  4 Hecke eigenvalues for primes up to 20
Equation [1,0,0,-10795601,259080456] [a1,a2,a3,a4,a6]
Generators [6316:425842:1] Generators of the group modulo torsion
j 1173340055458817/678770015625 j-invariant
L 4.2381858367205 L(r)(E,1)/r!
Ω 0.091719374176026 Real period
R 3.8506821077015 Regulator
r 1 Rank of the group of rational points
S 0.99999999997405 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 56355k1 Quadratic twists by: 17


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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