Cremona's table of elliptic curves

3380 = 2² · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2- 5- 13+	Signs for the Atkin-Lehner involutions
Class	3380i	Isogeny class
Conductor	3380	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	-19307236000000 = -1 · 28 · 56 · 136	Discriminant
Eigenvalues	2- -2 5- -2  0 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6140,-283100]	[a1,a2,a3,a4,a6]
Generators	[160:1690:1]	Generators of the group modulo torsion
j	-20720464/15625	j-invariant
L	2.428391222524	L(r)(E,1)/r!
Ω	0.26111357424306	Real period
R	0.5166741095887	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	13520bb4 54080o4 30420j4 16900j4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3380i4

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

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Quadratic twists for elliptic curve 3380i4

-4	8	-3	5	13
13520bb4	54080o4	30420j4	16900j4	20a3

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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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