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	13328i	Isogeny class
Conductor	13328	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	225792	Modular degree for the optimal curve
Δ	-605573322866962688 = -1 · 28 · 78 · 177	Discriminant
Eigenvalues	2- -1 -4 7+  3 -5 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-213460,-53246164]	[a1,a2,a3,a4,a6]
j	-728871512656/410338673	j-invariant
L	0.10823248253874	L(r)(E,1)/r!
Ω	0.10823248253874	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3332a1 53312bh1 119952eh1 13328r1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13328i1

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
-	-1	-4	+	3	-5	+	-6	4	8	0	-8	-8	-10	2	3	-2	-8	-14	-7	-8	-15	-12	1	18

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Quadratic twists for elliptic curve 13328i1

-4	8	-3	-7
3332a1	53312bh1	119952eh1	13328r1

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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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