Cremona's table of elliptic curves

2717 = 11 · 13 · 19

Field	Data	Notes
Atkin-Lehner	11+ 13- 19-	Signs for the Atkin-Lehner involutions
Class	2717c	Isogeny class
Conductor	2717	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	582413079677 = 119 · 13 · 19	Discriminant
Eigenvalues	0 -2  0 -1 11+ 13-  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-25563,-1581258]	[a1,a2,a3,a4,a6]
Generators	[-742:161:8]	Generators of the group modulo torsion
j	1847464752369664000/582413079677	j-invariant
L	1.7572720376652	L(r)(E,1)/r!
Ω	0.37757514707269	Real period
R	4.6540987967275	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	43472u3 24453k3 67925d3 29887e3	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 2717c3

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	0	-1	+	-	0	-	-3	3	5	11	12	-10	0	-12	15	8	-4	0	11	-1	-15	9	-10

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Quadratic twists for elliptic curve 2717c3

-4	-3	5	-11	13	-19
43472u3	24453k3	67925d3	29887e3	35321c3	51623b3

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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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