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	8372f	Isogeny class
Conductor	8372	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	-31059182336 = -1 · 28 · 74 · 133 · 23	Discriminant
Eigenvalues	2- -1  1 7- -3 13- -2  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-85,8513]	[a1,a2,a3,a4,a6]
Generators	[8:91:1]	Generators of the group modulo torsion
j	-268435456/121324931	j-invariant
L	3.6618777095494	L(r)(E,1)/r!
Ω	0.95111683239745	Real period
R	0.32084015906498	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	33488o1 75348m1 58604d1 108836d1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 8372f1

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	1	-	-3	-	-2	1	-	2	4	-2	10	6	-12	0	12	0	-11	-8	-4	6	1	18	-1

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Quadratic twists for elliptic curve 8372f1

-4	-3	-7	13
33488o1	75348m1	58604d1	108836d1

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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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