Cremona's table of elliptic curves

32307 = 3 · 11² · 89

Field	Data	Notes
Atkin-Lehner	3- 11+ 89-	Signs for the Atkin-Lehner involutions
Class	32307f	Isogeny class
Conductor	32307	Conductor
∏ cp	56	Product of Tamagawa factors cp
Δ	-50426129504619 = -1 · 314 · 113 · 892	Discriminant
Eigenvalues	-1 3-  2  0 11+  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-44547,-3638700]	[a1,a2,a3,a4,a6]
Generators	[444:7788:1]	Generators of the group modulo torsion
j	-7345166619518603/37885897449	j-invariant
L	5.0845579881897	L(r)(E,1)/r!
Ω	0.16425966230643	Real period
R	2.2110280049437	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	96921k2 32307e2	Quadratic twists by: -3 -11

Hecke Eigenvalues for elliptic curve 32307f2

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	-	2	0	+	2	-2	0	0	0	-4	6	0	8	0	6	-12	-10	-12	12	4	-10	-6	-	-2

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Quadratic twists for elliptic curve 32307f2

-3	-11
96921k2	32307e2

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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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