Cremona's table of elliptic curves

3136 = 2⁶ · 7²

Field	Data	Notes
Atkin-Lehner	2+ 7-	Signs for the Atkin-Lehner involutions
Class	3136m	Isogeny class
Conductor	3136	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	-1404928 = -1 · 212 · 73	Discriminant
Eigenvalues	2+ -2 -2 7- -4 -6 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9,55]	[a1,a2,a3,a4,a6]
Generators	[-3:8:1] [-1:8:1]	Generators of the group modulo torsion
j	-64	j-invariant
L	2.8792288575243	L(r)(E,1)/r!
Ω	2.28107599137	Real period
R	0.6311119989901	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3136i1 1568d1 28224ca1 78400co1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3136m1

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	-	-4	-6	-4	-6	-4	6	-4	6	4	-12	-12	-6	-6	6	-12	8	0	0	-6	-16	-12

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Quadratic twists for elliptic curve 3136m1

-4	8	-3	5	-7
3136i1	1568d1	28224ca1	78400co1	3136h1

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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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