Cremona's table of elliptic curves

Curve 67575f1

67575 = 3 · 52 · 17 · 53



Data for elliptic curve 67575f1

Field Data Notes
Atkin-Lehner 3+ 5- 17- 53- Signs for the Atkin-Lehner involutions
Class 67575f Isogeny class
Conductor 67575 Conductor
∏ cp 8 Product of Tamagawa factors cp
deg 116480 Modular degree for the optimal curve
Δ 269244140625 = 32 · 59 · 172 · 53 Discriminant
Eigenvalues -1 3+ 5- -2  0  0 17-  0 Hecke eigenvalues for primes up to 20
Equation [1,1,1,-39763,-3068344] [a1,a2,a3,a4,a6]
Generators [-116:63:1] [-922:525:8] Generators of the group modulo torsion
j 3559850710109/137853 j-invariant
L 5.5380279000925 L(r)(E,1)/r!
Ω 0.33808875105434 Real period
R 8.1901984061633 Regulator
r 2 Rank of the group of rational points
S 1.0000000000069 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 67575k1 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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