Cremona's table of elliptic curves

8372 = 2² · 7 · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 7+ 13+ 23+	Signs for the Atkin-Lehner involutions
Class	8372a	Isogeny class
Conductor	8372	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	5391568 = 24 · 72 · 13 · 232	Discriminant
Eigenvalues	2-  0  0 7+  0 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-220,-1251]	[a1,a2,a3,a4,a6]
j	73598976000/336973	j-invariant
L	1.2399767350385	L(r)(E,1)/r!
Ω	1.2399767350385	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33488z1 75348c1 58604i1 108836g1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 8372a1

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

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Quadratic twists for elliptic curve 8372a1

-4	-3	-7	13
33488z1	75348c1	58604i1	108836g1

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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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