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	1716a	Isogeny class
Conductor	1716	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	17102562048 = 28 · 33 · 114 · 132	Discriminant
Eigenvalues	2- 3+  0 -2 11+ 13- -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-668,2376]	[a1,a2,a3,a4,a6]
Generators	[25:26:1]	Generators of the group modulo torsion
j	128962402000/66806883	j-invariant
L	2.4130659473475	L(r)(E,1)/r!
Ω	1.0851456648809	Real period
R	2.2237253720332	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	6864z2 27456bd2 5148f2 42900x2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1716a2

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	+	-	-2	6	8	-2	-6	-6	-8	-8	12	-10	-8	2	6	-8	-2	12	8	0	-18

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Quadratic twists for elliptic curve 1716a2

-4	8	-3	5	-7	-11	13
6864z2	27456bd2	5148f2	42900x2	84084r2	18876b2	22308a2

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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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