Cremona's table of elliptic curves

32340 = 2² · 3 · 5 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	32340bg	Isogeny class
Conductor	32340	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	-87890156046000 = -1 · 24 · 32 · 53 · 79 · 112	Discriminant
Eigenvalues	2- 3- 5+ 7- 11- -2  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,10519,-172656]	[a1,a2,a3,a4,a6]
Generators	[27:363:1]	Generators of the group modulo torsion
j	199344128/136125	j-invariant
L	6.3074020828944	L(r)(E,1)/r!
Ω	0.34265288814586	Real period
R	3.067925929855	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	129360dv1 97020cn1 32340r1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 32340bg1

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	2	-6	0	2	4	-2	0	4	8	-4	-14	14	-2	-8	-10	-16	4	10	2

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Quadratic twists for elliptic curve 32340bg1

-4	-3	-7
129360dv1	97020cn1	32340r1

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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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