Cremona's table of elliptic curves

3245 = 5 · 11 · 59

Field	Data	Notes
Atkin-Lehner	5+ 11+ 59+	Signs for the Atkin-Lehner involutions
Class	3245a	Isogeny class
Conductor	3245	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	178475 = 52 · 112 · 59	Discriminant
Eigenvalues	1 -2 5+  4 11+  2  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-314,-2163]	[a1,a2,a3,a4,a6]
Generators	[21:14:1]	Generators of the group modulo torsion
j	3408183162649/178475	j-invariant
L	2.9942575423772	L(r)(E,1)/r!
Ω	1.1345778953289	Real period
R	2.6390938468875	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	51920t2 29205r2 16225a2 35695b2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3245a2

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
1	-2	+	4	+	2	2	-6	-4	6	0	-4	10	-4	8	-14	+	12	-8	-4	-6	-6	-12	-2	-8

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Quadratic twists for elliptic curve 3245a2

-4	-3	5	-11
51920t2	29205r2	16225a2	35695b2

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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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