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	39675bb	Isogeny class
Conductor	39675	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	18432	Modular degree for the optimal curve
Δ	3347578125 = 34 · 57 · 232	Discriminant
Eigenvalues	0 3- 5+ -2 -1 -6  2 -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-383,644]	[a1,a2,a3,a4,a6]
Generators	[-2:37:1]	Generators of the group modulo torsion
j	753664/405	j-invariant
L	4.2538614428747	L(r)(E,1)/r!
Ω	1.234157015005	Real period
R	0.21542343230817	Regulator
r	1	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	119025t1 7935e1 39675ba1	Quadratic twists by: -3 5 -23

Hecke Eigenvalues for elliptic curve 39675bb1

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
0	-	+	-2	-1	-6	2	-3	-	-10	3	4	9	8	6	0	0	-13	2	7	6	-5	-16	14	12

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Quadratic twists for elliptic curve 39675bb1

-3	5	-23
119025t1	7935e1	39675ba1

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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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