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	12	Product of Tamagawa factors cp
Δ	-352646875000 = -1 · 23 · 58 · 74 · 47	Discriminant
Eigenvalues	2-  0 5+ 7+  4  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,1367,20577]	[a1,a2,a3,a4,a6]
Generators	[97:980:1]	Generators of the group modulo torsion
j	282700817634591/352646875000	j-invariant
L	4.6089242428104	L(r)(E,1)/r!
Ω	0.64238723659637	Real period
R	2.391560718231	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	26320g3 105280m3 29610j3 16450d4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3290f4

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 3290f4

-4	8	-3	5	-7
26320g3	105280m3	29610j3	16450d4	23030u3

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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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