Cremona's table of elliptic curves

2492 = 2² · 7 · 89

Field	Data	Notes
Atkin-Lehner	2- 7+ 89-	Signs for the Atkin-Lehner involutions
Class	2492b	Isogeny class
Conductor	2492	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1248	Modular degree for the optimal curve
Δ	-54704384 = -1 · 28 · 74 · 89	Discriminant
Eigenvalues	2- -3  3 7+ -4  4 -5  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-31,-362]	[a1,a2,a3,a4,a6]
Generators	[22:98:1]	Generators of the group modulo torsion
j	-12869712/213689	j-invariant
L	2.3043399763985	L(r)(E,1)/r!
Ω	0.85453346240873	Real period
R	1.348302949953	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	9968p1 39872k1 22428c1 62300m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2492b1

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
-	-3	3	+	-4	4	-5	1	1	2	-7	-2	-6	-1	2	1	12	-8	-14	6	3	14	12	-	-3

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Quadratic twists for elliptic curve 2492b1

-4	8	-3	5	-7
9968p1	39872k1	22428c1	62300m1	17444c1

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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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