Cremona's table of elliptic curves

13328 = 2⁴ · 7² · 17

Field	Data	Notes
Atkin-Lehner	2- 7- 17-	Signs for the Atkin-Lehner involutions
Class	13328x	Isogeny class
Conductor	13328	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-7888470016 = -1 · 215 · 72 · 173	Discriminant
Eigenvalues	2- -2 -3 7-  0 -2 17- -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,488,-876]	[a1,a2,a3,a4,a6]
Generators	[38:-272:1] [60:498:1]	Generators of the group modulo torsion
j	63905303/39304	j-invariant
L	4.2008456525042	L(r)(E,1)/r!
Ω	0.76023766368077	Real period
R	0.4604750432215	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1666f2 53312cd2 119952fj2 13328j2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13328x2

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	-3	-	0	-2	-	-7	3	-6	-4	-7	-6	1	0	-6	9	-14	-5	15	-2	16	-12	-9	-14

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Quadratic twists for elliptic curve 13328x2

-4	8	-3	-7
1666f2	53312cd2	119952fj2	13328j2

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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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