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	13328c	Isogeny class
Conductor	13328	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	76608	Modular degree for the optimal curve
Δ	-2842216239794176 = -1 · 211 · 710 · 173	Discriminant
Eigenvalues	2+  0  1 7- -2  4 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-256907,-50185702]	[a1,a2,a3,a4,a6]
j	-3241463778/4913	j-invariant
L	1.6963134287446	L(r)(E,1)/r!
Ω	0.10601958929654	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6664c1 53312bq1 119952bg1 13328b1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13328c1

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	-	-2	4	+	5	-9	-6	8	-11	4	1	-2	6	9	-6	7	-1	-4	8	-4	15	0

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Quadratic twists for elliptic curve 13328c1

-4	8	-3	-7
6664c1	53312bq1	119952bg1	13328b1

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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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