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	3290a	Isogeny class
Conductor	3290	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2240	Modular degree for the optimal curve
Δ	210560000 = 210 · 54 · 7 · 47	Discriminant
Eigenvalues	2+ -2 5+ 7+  2 -6 -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-274,1572]	[a1,a2,a3,a4,a6]
Generators	[6:9:1]	Generators of the group modulo torsion
j	2263054145689/210560000	j-invariant
L	1.4965613159955	L(r)(E,1)/r!
Ω	1.7308241674043	Real period
R	0.86465242638707	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	26320i1 105280j1 29610be1 16450q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3290a1

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

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Quadratic twists for elliptic curve 3290a1

-4	8	-3	5	-7
26320i1	105280j1	29610be1	16450q1	23030p1

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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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