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	8372g	Isogeny class
Conductor	8372	Conductor
∏ cp	27	Product of Tamagawa factors cp
Δ	21416677261720832 = 28 · 73 · 139 · 23	Discriminant
Eigenvalues	2- -2  0 7- -3 13-  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-69893,980311]	[a1,a2,a3,a4,a6]
Generators	[-6:1183:1]	Generators of the group modulo torsion
j	147499655667712000/83658895553597	j-invariant
L	2.8605811321092	L(r)(E,1)/r!
Ω	0.3290221028897	Real period
R	0.32200708829855	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	33488q2 75348l2 58604g2 108836e2	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 8372g2

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	0	-	-3	-	3	-4	-	-3	5	5	3	2	0	-6	3	-1	5	6	-13	-4	12	-18	-10

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Quadratic twists for elliptic curve 8372g2

-4	-3	-7	13
33488q2	75348l2	58604g2	108836e2

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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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