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	3380h	Isogeny class
Conductor	3380	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-882294347833600 = -1 · 28 · 52 · 1310	Discriminant
Eigenvalues	2-  2 5- -2 -4 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-46700,4154552]	[a1,a2,a3,a4,a6]
Generators	[334:5070:1]	Generators of the group modulo torsion
j	-9115564624/714025	j-invariant
L	4.5800194602745	L(r)(E,1)/r!
Ω	0.48936182839858	Real period
R	1.5598612977445	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	13520bd2 54080r2 30420k2 16900m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3380h2

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	-4	+	2	0	-6	-10	0	-10	2	2	6	2	8	2	6	8	-10	-16	-6	-10	-2

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Quadratic twists for elliptic curve 3380h2

-4	8	-3	5	13
13520bd2	54080r2	30420k2	16900m2	260a2

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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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