Cremona's table of elliptic curves

2142 = 2 · 3² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 17+	Signs for the Atkin-Lehner involutions
Class	2142g	Isogeny class
Conductor	2142	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	40436496888496128 = 224 · 310 · 74 · 17	Discriminant
Eigenvalues	2+ 3-  2 7- -4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-632196,-193075376]	[a1,a2,a3,a4,a6]
Generators	[-447:451:1]	Generators of the group modulo torsion
j	38331145780597164097/55468445663232	j-invariant
L	2.5663010016199	L(r)(E,1)/r!
Ω	0.16932626500501	Real period
R	3.7889883792452	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	17136y1 68544ca1 714g1 53550dt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2142g1

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

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Quadratic twists for elliptic curve 2142g1

-4	8	-3	5	-7	17
17136y1	68544ca1	714g1	53550dt1	14994bi1	36414t1

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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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