Cremona's table of elliptic curves

39675 = 3 · 5² · 23²

Field	Data	Notes
Atkin-Lehner	3+ 5+ 23-	Signs for the Atkin-Lehner involutions
Class	39675r	Isogeny class
Conductor	39675	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	371953125 = 32 · 57 · 232	Discriminant
Eigenvalues	-2 3+ 5+ -2  1 -4  0  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-3258,72668]	[a1,a2,a3,a4,a6]
Generators	[32:12:1] [-12:331:1]	Generators of the group modulo torsion
j	462843904/45	j-invariant
L	3.9128677623961	L(r)(E,1)/r!
Ω	1.6238381639889	Real period
R	0.30120518235512	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	119025bq1 7935l1 39675q1	Quadratic twists by: -3 5 -23

Hecke Eigenvalues for elliptic curve 39675r1

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	1	-4	0	1	-	-6	-1	-6	3	-2	-10	-10	8	7	-10	-15	6	-5	-6	-6	-2

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Quadratic twists for elliptic curve 39675r1

-3	5	-23
119025bq1	7935l1	39675q1

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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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