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	18	Product of Tamagawa factors cp
Δ	9653618000 = 24 · 53 · 136	Discriminant
Eigenvalues	2- -2 5- -2  0 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-6985,-226992]	[a1,a2,a3,a4,a6]
Generators	[-49:5:1]	Generators of the group modulo torsion
j	488095744/125	j-invariant
L	2.428391222524	L(r)(E,1)/r!
Ω	0.52222714848613	Real period
R	1.0333482191774	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	13520bb3 54080o3 30420j3 16900j3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3380i3

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 3380i3

-4	8	-3	5	13
13520bb3	54080o3	30420j3	16900j3	20a4

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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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