Cremona's table of elliptic curves

3124 = 2² · 11 · 71

Field	Data	Notes
Atkin-Lehner	2- 11- 71+	Signs for the Atkin-Lehner involutions
Class	3124a	Isogeny class
Conductor	3124	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	264	Modular degree for the optimal curve
Δ	199936 = 28 · 11 · 71	Discriminant
Eigenvalues	2-  0  3 -1 11- -5  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-16,-12]	[a1,a2,a3,a4,a6]
Generators	[-3:3:1]	Generators of the group modulo torsion
j	1769472/781	j-invariant
L	3.7406901227004	L(r)(E,1)/r!
Ω	2.4863090670162	Real period
R	1.5045153365384	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	12496f1 49984a1 28116f1 78100b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3124a1

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	3	-2	-4	0	-2	-11	-3	10	-2	4	4	-7	-12	+	-4	-14	-2	9	-18

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Quadratic twists for elliptic curve 3124a1

-4	8	-3	5	-11
12496f1	49984a1	28116f1	78100b1	34364a1

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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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