Cremona's table of elliptic curves

Curve 51520bc1

51520 = 26 · 5 · 7 · 23



Data for elliptic curve 51520bc1

Field Data Notes
Atkin-Lehner 2+ 5- 7+ 23- Signs for the Atkin-Lehner involutions
Class 51520bc Isogeny class
Conductor 51520 Conductor
∏ cp 32 Product of Tamagawa factors cp
deg 196608 Modular degree for the optimal curve
Δ 201958400000000 = 216 · 58 · 73 · 23 Discriminant
Eigenvalues 2+  2 5- 7+  6 -4  2  4 Hecke eigenvalues for primes up to 20
Equation [0,-1,0,-17185,-527583] [a1,a2,a3,a4,a6]
Generators [339:5700:1] Generators of the group modulo torsion
j 8564808605476/3081640625 j-invariant
L 9.9784612898899 L(r)(E,1)/r!
Ω 0.42944656260349 Real period
R 2.9044537082132 Regulator
r 1 Rank of the group of rational points
S 1.0000000000025 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 51520ci1 6440f1 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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