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	8112be	Isogeny class
Conductor	8112	Conductor
∏ cp	42	Product of Tamagawa factors cp
deg	26208	Modular degree for the optimal curve
Δ	-456704790227712 = -1 · 28 · 37 · 138	Discriminant
Eigenvalues	2- 3-  2 -1 -2 13+ -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11717,1134303]	[a1,a2,a3,a4,a6]
Generators	[-113:1014:1]	Generators of the group modulo torsion
j	-851968/2187	j-invariant
L	5.4390454610096	L(r)(E,1)/r!
Ω	0.46583757521934	Real period
R	0.27799621433289	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	2028a1 32448ck1 24336bu1 8112bf1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112be1

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	-1	-2	+	-4	-4	-6	6	1	10	-4	-1	10	8	2	-5	7	-10	-7	-17	-12	-16	13

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Quadratic twists for elliptic curve 8112be1

-4	8	-3	13
2028a1	32448ck1	24336bu1	8112bf1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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