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	8112w	Isogeny class
Conductor	8112	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1.3663793399246E+20	Discriminant
Eigenvalues	2- 3+  2 -2  0 13-  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-11996352,-15998592000]	[a1,a2,a3,a4,a6]
Generators	[748518561367613062637092035394720:-43751993839793062627157391129608192:126717908222032835464132447625]	Generators of the group modulo torsion
j	-4395631034341/3145728	j-invariant
L	3.9584029325211	L(r)(E,1)/r!
Ω	0.040559128641142	Real period
R	48.797928667849	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	1014g3 32448dm3 24336ce3 8112y3	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 8112w3

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

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Quadratic twists for elliptic curve 8112w3

-4	8	-3	13
1014g3	32448dm3	24336ce3	8112y3

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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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