Cremona's table of elliptic curves

6960 = 2⁴ · 3 · 5 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 29-	Signs for the Atkin-Lehner involutions
Class	6960f	Isogeny class
Conductor	6960	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	33408000 = 210 · 32 · 53 · 29	Discriminant
Eigenvalues	2+ 3+ 5+  2  2  4 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1216,-15920]	[a1,a2,a3,a4,a6]
j	194348673796/32625	j-invariant
L	1.616853879023	L(r)(E,1)/r!
Ω	0.8084269395115	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3480h1 27840dz1 20880t1 34800bg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6960f1

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	-8	4	-	10	2	0	-4	8	6	12	-12	-12	16	2	-2	-6	0	-10

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Quadratic twists for elliptic curve 6960f1

-4	8	-3	5
3480h1	27840dz1	20880t1	34800bg1

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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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