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	8112m	Isogeny class
Conductor	8112	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	421573652517888 = 210 · 38 · 137	Discriminant
Eigenvalues	2+ 3-  2  4  0 13+  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-51432,4362372]	[a1,a2,a3,a4,a6]
j	3044193988/85293	j-invariant
L	4.2299470107962	L(r)(E,1)/r!
Ω	0.52874337634952	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4056m3 32448cl4 24336l4 624f3	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112m3

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

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Quadratic twists for elliptic curve 8112m3

-4	8	-3	13
4056m3	32448cl4	24336l4	624f3

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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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