Cremona's table of elliptic curves

Curve 1692a1

1692 = 22 · 32 · 47



Data for elliptic curve 1692a1

Field Data Notes
Atkin-Lehner 2- 3+ 47+ Signs for the Atkin-Lehner involutions
Class 1692a Isogeny class
Conductor 1692 Conductor
∏ cp 2 Product of Tamagawa factors cp
deg 576 Modular degree for the optimal curve
Δ 236825856 = 28 · 39 · 47 Discriminant
Eigenvalues 2- 3+  3  3 -1 -4  4  4 Hecke eigenvalues for primes up to 20
Equation [0,0,0,-216,-972] [a1,a2,a3,a4,a6]
j 221184/47 j-invariant
L 2.5281216762696 L(r)(E,1)/r!
Ω 1.2640608381348 Real period
R 1 Regulator
r 0 Rank of the group of rational points
S 1 (Analytic) order of Ш
t 1 Number of elements in the torsion subgroup
Twists 6768j1 27072d1 1692b1 42300d1 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
Back to Tables and computations