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	3380f	Isogeny class
Conductor	3380	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	7140250000 = 24 · 56 · 134	Discriminant
Eigenvalues	2-  1 5- -1  3 13+ -3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1070,-13207]	[a1,a2,a3,a4,a6]
Generators	[-22:13:1]	Generators of the group modulo torsion
j	296747776/15625	j-invariant
L	4.1082947421098	L(r)(E,1)/r!
Ω	0.83741358785034	Real period
R	0.81765545757302	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	13520y1 54080l1 30420h1 16900g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3380f1

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	-	-1	3	+	-3	-7	-3	3	-4	-7	-9	11	0	-6	-3	11	-7	-3	2	8	-12	15	-7

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Quadratic twists for elliptic curve 3380f1

-4	8	-3	5	13
13520y1	54080l1	30420h1	16900g1	3380a1

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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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