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	3952f	Isogeny class
Conductor	3952	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3648	Modular degree for the optimal curve
Δ	-38445056 = -1 · 213 · 13 · 192	Discriminant
Eigenvalues	2- -3 -3 -3  0 13+  5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-979,11794]	[a1,a2,a3,a4,a6]
Generators	[-15:152:1] [1:104:1]	Generators of the group modulo torsion
j	-25334470953/9386	j-invariant
L	2.5744345260114	L(r)(E,1)/r!
Ω	2.011556617816	Real period
R	0.15997775697752	Regulator
r	2	Rank of the group of rational points
S	0.99999999999985	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	494c1 15808z1 35568bp1 98800by1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3952f1

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
-	-3	-3	-3	0	+	5	+	-6	-8	-8	-5	-10	-7	1	-10	-6	-6	4	5	8	-12	8	0	-2

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Quadratic twists for elliptic curve 3952f1

-4	8	-3	5	13	-19
494c1	15808z1	35568bp1	98800by1	51376z1	75088bg1

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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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