Cremona's table of elliptic curves

3975 = 3 · 5² · 53

Field	Data	Notes
Atkin-Lehner	3- 5- 53+	Signs for the Atkin-Lehner involutions
Class	3975m	Isogeny class
Conductor	3975	Conductor
∏ cp	22	Product of Tamagawa factors cp
deg	5544	Modular degree for the optimal curve
Δ	-311003701875 = -1 · 311 · 54 · 532	Discriminant
Eigenvalues	0 3- 5- -3 -4  5  0  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-8783,315044]	[a1,a2,a3,a4,a6]
Generators	[34:238:1]	Generators of the group modulo torsion
j	-119900719513600/497605923	j-invariant
L	3.2587346067098	L(r)(E,1)/r!
Ω	0.97265569559445	Real period
R	0.15228852406448	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	63600cm1 11925y1 3975c1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 3975m1

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	-	-	-3	-4	5	0	1	2	-4	11	2	-6	1	-6	+	4	-11	-5	-16	-10	4	0	14	-7

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Quadratic twists for elliptic curve 3975m1

-4	-3	5
63600cm1	11925y1	3975c1

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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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