Cremona's table of elliptic curves

3952 = 2⁴ · 13 · 19

Field	Data	Notes
Atkin-Lehner	2+ 13+ 19+	Signs for the Atkin-Lehner involutions
Class	3952a	Isogeny class
Conductor	3952	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	-3952 = -1 · 24 · 13 · 19	Discriminant
Eigenvalues	2+ -2  0  2  4 13+ -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8,7]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	-4000000/247	j-invariant
L	2.7610898120358	L(r)(E,1)/r!
Ω	4.3388538597599	Real period
R	0.63636386503891	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	1976b1 15808x1 35568f1 98800o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3952a1

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	0	2	4	+	-3	+	-1	-2	-3	-5	7	3	2	-6	-1	-5	-3	12	0	10	-18	10	13

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Quadratic twists for elliptic curve 3952a1

-4	8	-3	5	13	-19
1976b1	15808x1	35568f1	98800o1	51376f1	75088l1

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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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