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	2492c	Isogeny class
Conductor	2492	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	2784	Modular degree for the optimal curve
Δ	-433313425664 = -1 · 28 · 74 · 893	Discriminant
Eigenvalues	2-  1  3 7-  0 -4  3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,356,31684]	[a1,a2,a3,a4,a6]
j	19436284208/1692630569	j-invariant
L	2.8825745110072	L(r)(E,1)/r!
Ω	0.72064362775181	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	9968h1 39872u1 22428f1 62300d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2492c1

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
-	1	3	-	0	-4	3	5	-3	6	5	2	6	11	6	9	-12	8	-10	6	11	2	12	-	-19

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Quadratic twists for elliptic curve 2492c1

-4	8	-3	5	-7
9968h1	39872u1	22428f1	62300d1	17444b1

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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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