Cremona's table of elliptic curves

Curve 21675x1

21675 = 3 · 52 · 172



Data for elliptic curve 21675x1

Field Data Notes
Atkin-Lehner 3- 5- 17+ Signs for the Atkin-Lehner involutions
Class 21675x Isogeny class
Conductor 21675 Conductor
∏ cp 40 Product of Tamagawa factors cp
deg 92160 Modular degree for the optimal curve
Δ -211888632270375 = -1 · 35 · 53 · 178 Discriminant
Eigenvalues -1 3- 5- -4 -6 -4 17+  4 Hecke eigenvalues for primes up to 20
Equation [1,0,0,-873,-700488] [a1,a2,a3,a4,a6]
Generators [177:2079:1] Generators of the group modulo torsion
j -24389/70227 j-invariant
L 2.438597976072 L(r)(E,1)/r!
Ω 0.25479412487882 Real period
R 0.95708563815271 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 65025cd1 21675k1 1275b1 Quadratic twists by: -3 5 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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