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	1716b	Isogeny class
Conductor	1716	Conductor
∏ cp	324	Product of Tamagawa factors cp
deg	7776	Modular degree for the optimal curve
Δ	1647851208548688 = 24 · 318 · 112 · 133	Discriminant
Eigenvalues	2- 3-  0  2 11+ 13-  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-95173,-11162788]	[a1,a2,a3,a4,a6]
j	5958673237147648000/102990700534293	j-invariant
L	2.448886400355	L(r)(E,1)/r!
Ω	0.27209848892833	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	6864p1 27456m1 5148e1 42900b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1716b1

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	+	-	6	2	0	6	-10	2	0	8	12	6	0	2	2	0	-10	-4	0	0	14

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Quadratic twists for elliptic curve 1716b1

-4	8	-3	5	-7	-11	13
6864p1	27456m1	5148e1	42900b1	84084e1	18876i1	22308f1

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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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