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	8112s	Isogeny class
Conductor	8112	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	45556992 = 28 · 34 · 133	Discriminant
Eigenvalues	2+ 3-  0 -2 -2 13- -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-108,-324]	[a1,a2,a3,a4,a6]
Generators	[-6:12:1]	Generators of the group modulo torsion
j	250000/81	j-invariant
L	4.7472928001353	L(r)(E,1)/r!
Ω	1.5179317341014	Real period
R	0.78186862648104	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4056o2 32448ct2 24336t2 8112r2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112s2

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	-2	-	-2	6	0	-2	2	4	4	-4	10	-10	6	-2	-2	6	-16	-8	-14	12	-8

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Quadratic twists for elliptic curve 8112s2

-4	8	-3	13
4056o2	32448ct2	24336t2	8112r2

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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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