Cremona's table of elliptic curves

1716 = 2² · 3 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 13-	Signs for the Atkin-Lehner involutions
Class	1716c	Isogeny class
Conductor	1716	Conductor
∏ cp	84	Product of Tamagawa factors cp
deg	1344	Modular degree for the optimal curve
Δ	-142264629936 = -1 · 24 · 314 · 11 · 132	Discriminant
Eigenvalues	2- 3- -2 -2 11- 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-109,18116]	[a1,a2,a3,a4,a6]
Generators	[-19:117:1]	Generators of the group modulo torsion
j	-9033613312/8891539371	j-invariant
L	2.9769833811169	L(r)(E,1)/r!
Ω	0.83389797969491	Real period
R	0.16999814945994	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	6864m1 27456a1 5148c1 42900f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1716c1

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	-2	-	-	0	2	-8	-4	4	-6	0	-6	0	-2	-12	-6	8	-8	-2	-14	0	-2	14

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Quadratic twists for elliptic curve 1716c1

-4	8	-3	5	-7	-11	13
6864m1	27456a1	5148c1	42900f1	84084l1	18876j1	22308d1

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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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