Cremona's table of elliptic curves

3116 = 2² · 19 · 41

Field	Data	Notes
Atkin-Lehner	2- 19+ 41-	Signs for the Atkin-Lehner involutions
Class	3116a	Isogeny class
Conductor	3116	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-8176384 = -1 · 28 · 19 · 412	Discriminant
Eigenvalues	2-  0  3 -1 -5  0  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-56,212]	[a1,a2,a3,a4,a6]
Generators	[13:41:1]	Generators of the group modulo torsion
j	-75866112/31939	j-invariant
L	3.67141086835	L(r)(E,1)/r!
Ω	2.1841499350951	Real period
R	0.84046676680877	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	12464d1 49856f1 28044a1 77900a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3116a1

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	3	-1	-5	0	3	+	0	2	-2	2	-	1	-7	-4	-10	-5	-8	-10	-7	10	-4	-2	-10

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Quadratic twists for elliptic curve 3116a1

-4	8	-3	5	-19	41
12464d1	49856f1	28044a1	77900a1	59204c1	127756a1

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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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