Cremona's table of elliptic curves

Curve 3192p1

3192 = 23 · 3 · 7 · 19



Data for elliptic curve 3192p1

Field Data Notes
Atkin-Lehner 2- 3- 7- 19- Signs for the Atkin-Lehner involutions
Class 3192p Isogeny class
Conductor 3192 Conductor
∏ cp 24 Product of Tamagawa factors cp
deg 1152 Modular degree for the optimal curve
Δ 6435072 = 28 · 33 · 72 · 19 Discriminant
Eigenvalues 2- 3- -4 7-  2 -4  4 19- Hecke eigenvalues for primes up to 20
Equation [0,1,0,-180,864] [a1,a2,a3,a4,a6]
Generators [-6:42:1] Generators of the group modulo torsion
j 2533446736/25137 j-invariant
L 3.3369755712577 L(r)(E,1)/r!
Ω 2.3886993668732 Real period
R 0.23283072073555 Regulator
r 1 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 6384a1 25536o1 9576m1 79800b1 Quadratic twists by: -4 8 -3 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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