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	13328b	Isogeny class
Conductor	13328	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	10944	Modular degree for the optimal curve
Δ	-24158439424 = -1 · 211 · 74 · 173	Discriminant
Eigenvalues	2+  0 -1 7+ -2 -4 17- -5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5243,146314]	[a1,a2,a3,a4,a6]
Generators	[-63:476:1] [39:34:1]	Generators of the group modulo torsion
j	-3241463778/4913	j-invariant
L	6.0627999966283	L(r)(E,1)/r!
Ω	1.1965070384622	Real period
R	0.1407522944737	Regulator
r	2	Rank of the group of rational points
S	0.99999999999982	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6664b1 53312bo1 119952m1 13328c1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13328b1

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 13328b1

-4	8	-3	-7
6664b1	53312bo1	119952m1	13328c1

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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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