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	13328n	Isogeny class
Conductor	13328	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	7488	Modular degree for the optimal curve
Δ	-27950841856 = -1 · 225 · 72 · 17	Discriminant
Eigenvalues	2-  0  1 7-  6 -4 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,133,-8022]	[a1,a2,a3,a4,a6]
Generators	[74:638:1]	Generators of the group modulo torsion
j	1296351/139264	j-invariant
L	5.0123209498732	L(r)(E,1)/r!
Ω	0.56103850095385	Real period
R	4.4670026578849	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1666j1 53312br1 119952gk1 13328m1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13328n1

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
-	0	1	-	6	-4	+	1	3	-6	0	-3	12	-3	-10	-2	13	10	3	3	4	-16	-12	-1	-16

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Quadratic twists for elliptic curve 13328n1

-4	8	-3	-7
1666j1	53312br1	119952gk1	13328m1

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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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