Cremona's table of elliptic curves

8112 = 2⁴ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13-	Signs for the Atkin-Lehner involutions
Class	8112g	Isogeny class
Conductor	8112	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	20247552 = 210 · 32 · 133	Discriminant
Eigenvalues	2+ 3+ -2 -2 -4 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-264,1728]	[a1,a2,a3,a4,a6]
Generators	[-16:40:1] [-4:52:1]	Generators of the group modulo torsion
j	907924/9	j-invariant
L	4.322476400594	L(r)(E,1)/r!
Ω	2.1710909919712	Real period
R	0.49773091231307	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	4056r2 32448dj2 24336u2 8112f2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112g2

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	-2	-4	6	-2	-8	6	-4	-8	2	-8	-14	-14	-12	-4	0	0	-6	12

---

Quadratic twists for elliptic curve 8112g2

-4	8	-3	13
4056r2	32448dj2	24336u2	8112f2

---

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