Cremona's table of elliptic curves

Curve 18564a1

18564 = 22 · 3 · 7 · 13 · 17



Data for elliptic curve 18564a1

Field Data Notes
Atkin-Lehner 2- 3+ 7+ 13+ 17+ Signs for the Atkin-Lehner involutions
Class 18564a Isogeny class
Conductor 18564 Conductor
∏ cp 24 Product of Tamagawa factors cp
deg 5760 Modular degree for the optimal curve
Δ 26509392 = 24 · 32 · 72 · 13 · 172 Discriminant
Eigenvalues 2- 3+ -2 7+ -2 13+ 17+  2 Hecke eigenvalues for primes up to 20
Equation [0,-1,0,-229,1390] [a1,a2,a3,a4,a6]
Generators [-15:35:1] [-7:51:1] Generators of the group modulo torsion
j 83369132032/1656837 j-invariant
L 5.6118556306767 L(r)(E,1)/r!
Ω 2.1134848484571 Real period
R 0.44254363709409 Regulator
r 2 Rank of the group of rational points
S 0.99999999999998 (Analytic) order of Ш
t 2 Number of elements in the torsion subgroup
Twists 74256cv1 55692o1 129948bm1 Quadratic twists by: -4 -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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