Cremona's table of elliptic curves

Curve 57222r1

57222 = 2 · 32 · 11 · 172



Data for elliptic curve 57222r1

Field Data Notes
Atkin-Lehner 2+ 3- 11- 17+ Signs for the Atkin-Lehner involutions
Class 57222r Isogeny class
Conductor 57222 Conductor
∏ cp 32 Product of Tamagawa factors cp
deg 589824 Modular degree for the optimal curve
Δ 671263187032548 = 22 · 37 · 11 · 178 Discriminant
Eigenvalues 2+ 3-  0 -2 11-  4 17+ -8 Hecke eigenvalues for primes up to 20
Equation [1,-1,0,-515052,-142139588] [a1,a2,a3,a4,a6]
Generators [1254:33764:1] Generators of the group modulo torsion
j 858729462625/38148 j-invariant
L 4.0248108537669 L(r)(E,1)/r!
Ω 0.17821239358573 Real period
R 2.8230435975194 Regulator
r 1 Rank of the group of rational points
S 1.00000000002 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 19074m1 3366d1 Quadratic twists by: -3 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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