Cremona's table of elliptic curves

Curve 50715k1

50715 = 32 · 5 · 72 · 23



Data for elliptic curve 50715k1

Field Data Notes
Atkin-Lehner 3- 5+ 7- 23+ Signs for the Atkin-Lehner involutions
Class 50715k Isogeny class
Conductor 50715 Conductor
∏ cp 8 Product of Tamagawa factors cp
deg 3594240 Modular degree for the optimal curve
Δ -8.2590508850504E+23 Discriminant
Eigenvalues  0 3- 5+ 7- -1  0  2  3 Hecke eigenvalues for primes up to 20
Equation [0,0,1,12863382,-39956099927] [a1,a2,a3,a4,a6]
Generators [79131749:4623377243:24389] Generators of the group modulo torsion
j 2744564518708084736/9629735831296875 j-invariant
L 4.3411547377893 L(r)(E,1)/r!
Ω 0.045440176989977 Real period
R 11.941950453688 Regulator
r 1 Rank of the group of rational points
S 1.0000000000047 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 16905n1 7245l1 Quadratic twists by: -3 -7


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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