Cremona's table of elliptic curves

32160 = 2⁵ · 3 · 5 · 67

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 67+	Signs for the Atkin-Lehner involutions
Class	32160q	Isogeny class
Conductor	32160	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5632	Modular degree for the optimal curve
Δ	8040000 = 26 · 3 · 54 · 67	Discriminant
Eigenvalues	2- 3+ 5- -2 -4 -4  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-50,0]	[a1,a2,a3,a4,a6]
Generators	[-5:10:1]	Generators of the group modulo torsion
j	220348864/125625	j-invariant
L	3.8713952021649	L(r)(E,1)/r!
Ω	1.9390734184165	Real period
R	0.99825905646378	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	32160k1 64320bd1 96480f1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 32160q1

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	-4	-4	2	4	-6	-4	2	6	6	12	2	-2	-12	8	+	-2	-6	-10	-4	10	-14

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Quadratic twists for elliptic curve 32160q1

-4	8	-3
32160k1	64320bd1	96480f1

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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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