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	12696d	Isogeny class
Conductor	12696	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	50688	Modular degree for the optimal curve
Δ	-2541688576883712 = -1 · 210 · 36 · 237	Discriminant
Eigenvalues	2+ 3+  2 -2  2 -2  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-34032,3435228]	[a1,a2,a3,a4,a6]
j	-28756228/16767	j-invariant
L	1.6943608603103	L(r)(E,1)/r!
Ω	0.42359021507757	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25392k1 101568bn1 38088y1 552a1	Quadratic twists by: -4 8 -3 -23

Hecke Eigenvalues for elliptic curve 12696d1

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	2	-2	4	0	-	-10	0	4	-6	4	8	6	4	-8	4	8	6	-6	6	4	-10

---

Quadratic twists for elliptic curve 12696d1

-4	8	-3	-23
25392k1	101568bn1	38088y1	552a1

---

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