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	13328y	Isogeny class
Conductor	13328	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	129024	Modular degree for the optimal curve
Δ	6576777187033088 = 226 · 78 · 17	Discriminant
Eigenvalues	2- -2  4 7-  6  2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-47056,445332]	[a1,a2,a3,a4,a6]
j	23912763841/13647872	j-invariant
L	2.895493495327	L(r)(E,1)/r!
Ω	0.36193668691587	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1666m1 53312cf1 119952fx1 1904a1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13328y1

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	4	-	6	2	-	0	4	8	0	4	2	8	-8	-6	-4	8	16	-4	-10	12	12	-10	-6

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Quadratic twists for elliptic curve 13328y1

-4	8	-3	-7
1666m1	53312cf1	119952fx1	1904a1

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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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