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	8112t	Isogeny class
Conductor	8112	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	17892929374065408 = 28 · 3 · 1312	Discriminant
Eigenvalues	2- 3+  0  2  0 13+ -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-126468,16112316]	[a1,a2,a3,a4,a6]
j	181037698000/14480427	j-invariant
L	1.5179682393031	L(r)(E,1)/r!
Ω	0.37949205982578	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2028d4 32448cy4 24336bh4 624g4	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112t4

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
-	+	0	2	0	+	-6	2	0	-6	2	-2	12	4	0	6	12	2	-10	12	-14	-8	12	0	10

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Quadratic twists for elliptic curve 8112t4

-4	8	-3	13
2028d4	32448cy4	24336bh4	624g4

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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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