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	8112bd	Isogeny class
Conductor	8112	Conductor
∏ cp	84	Product of Tamagawa factors cp
Δ	-1.5981014019648E+19	Discriminant
Eigenvalues	2- 3- -1 -2  2 13+ -7  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-202856,195456756]	[a1,a2,a3,a4,a6]
Generators	[-620:9126:1]	Generators of the group modulo torsion
j	-276301129/4782969	j-invariant
L	4.58688577056	L(r)(E,1)/r!
Ω	0.18590403752511	Real period
R	0.2937310222511	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	507a2 32448cb2 24336bj2 8112ba2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112bd2

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
-	-	-1	-2	2	+	-7	6	6	-1	-4	1	9	-6	-6	-9	0	1	2	-6	11	4	14	-14	-2

---

Quadratic twists for elliptic curve 8112bd2

-4	8	-3	13
507a2	32448cb2	24336bj2	8112ba2

---

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