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	3380d	Isogeny class
Conductor	3380	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	67600 = 24 · 52 · 132	Discriminant
Eigenvalues	2- -3 5+ -3 -3 13+ -7 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-13,13]	[a1,a2,a3,a4,a6]
Generators	[-3:5:1] [-1:5:1]	Generators of the group modulo torsion
j	89856/25	j-invariant
L	2.6470132720516	L(r)(E,1)/r!
Ω	3.2395059193084	Real period
R	0.13618400140779	Regulator
r	2	Rank of the group of rational points
S	0.99999999999911	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13520u1 54080bt1 30420w1 16900n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3380d1

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
-	-3	+	-3	-3	+	-7	-1	-7	-5	4	3	-7	-9	-8	-6	-5	-5	-13	3	14	-8	-12	-7	11

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Quadratic twists for elliptic curve 3380d1

-4	8	-3	5	13
13520u1	54080bt1	30420w1	16900n1	3380j1

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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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