Cremona's table of elliptic curves

3290 = 2 · 5 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 47-	Signs for the Atkin-Lehner involutions
Class	3290f	Isogeny class
Conductor	3290	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	33689600 = 212 · 52 · 7 · 47	Discriminant
Eigenvalues	2-  0 5+ 7+  4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-193,-943]	[a1,a2,a3,a4,a6]
Generators	[-7:8:1]	Generators of the group modulo torsion
j	791196465249/33689600	j-invariant
L	4.6089242428104	L(r)(E,1)/r!
Ω	1.2847744731927	Real period
R	0.59789017955774	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	26320g1 105280m1 29610j1 16450d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3290f1

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	+	+	4	2	-6	-4	4	-6	-8	-2	-2	-4	-	6	-8	10	-4	0	6	-8	-16	-14	-6

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Quadratic twists for elliptic curve 3290f1

-4	8	-3	5	-7
26320g1	105280m1	29610j1	16450d1	23030u1

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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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