Cremona's table of elliptic curves

12696 = 2³ · 3 · 23²

Field	Data	Notes
Atkin-Lehner	2- 3- 23-	Signs for the Atkin-Lehner involutions
Class	12696s	Isogeny class
Conductor	12696	Conductor
∏ cp	80	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-183922990848 = -1 · 28 · 310 · 233	Discriminant
Eigenvalues	2- 3- -2 -2 -4 -6 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7444,245600]	[a1,a2,a3,a4,a6]
Generators	[-46:702:1] [8:432:1]	Generators of the group modulo torsion
j	-14647977776/59049	j-invariant
L	6.3867465876279	L(r)(E,1)/r!
Ω	1.0160969965156	Real period
R	0.31427839121311	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	25392d1 101568i1 38088e1 12696p1	Quadratic twists by: -4 8 -3 -23

Hecke Eigenvalues for elliptic curve 12696s1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	-2	-2	-4	-6	-6	-6	-	-6	8	-8	-6	10	4	2	8	-8	-10	-8	-10	-6	-12	-18	12

---

Quadratic twists for elliptic curve 12696s1

-4	8	-3	-23
25392d1	101568i1	38088e1	12696p1

---

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