Cremona's table of elliptic curves

3136 = 2⁶ · 7²

Field	Data	Notes
Atkin-Lehner	2+ 7+	Signs for the Atkin-Lehner involutions
Class	3136c	Isogeny class
Conductor	3136	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	5903156224 = 210 · 78	Discriminant
Eigenvalues	2+ -3  1 7+  1 -2  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1372,-19208]	[a1,a2,a3,a4,a6]
Generators	[-19:1:1]	Generators of the group modulo torsion
j	48384	j-invariant
L	2.2258441732993	L(r)(E,1)/r!
Ω	0.78542871383076	Real period
R	2.8339225878861	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	3136q1 392e1 28224y1 78400o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3136c1

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
+	-3	1	+	1	-2	3	-5	-3	6	-1	5	-10	4	1	9	-3	-3	-11	16	7	-11	4	-9	6

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Quadratic twists for elliptic curve 3136c1

-4	8	-3	5	-7
3136q1	392e1	28224y1	78400o1	3136n1

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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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