Cremona's table of elliptic curves

3948 = 2² · 3 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 47+	Signs for the Atkin-Lehner involutions
Class	3948b	Isogeny class
Conductor	3948	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	233747119872 = 28 · 310 · 7 · 472	Discriminant
Eigenvalues	2- 3- -2 7+ -4  4 -4  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3844,-90028]	[a1,a2,a3,a4,a6]
Generators	[-37:54:1]	Generators of the group modulo torsion
j	24544085702992/913074687	j-invariant
L	3.6870772139522	L(r)(E,1)/r!
Ω	0.60769735851297	Real period
R	1.2134583645302	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15792y2 63168c2 11844d2 98700n2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3948b2

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	+	-4	4	-4	8	4	-6	4	-6	2	-6	+	-6	-4	10	2	-10	0	-12	-8	-12	-10

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Quadratic twists for elliptic curve 3948b2

-4	8	-3	5	-7
15792y2	63168c2	11844d2	98700n2	27636k2

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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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