Cremona's table of elliptic curves

1496 = 2³ · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 11+ 17-	Signs for the Atkin-Lehner involutions
Class	1496d	Isogeny class
Conductor	1496	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-28458611456 = -1 · 28 · 113 · 174	Discriminant
Eigenvalues	2-  1  1 -2 11+ -4 17-  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2265,41531]	[a1,a2,a3,a4,a6]
Generators	[25:34:1]	Generators of the group modulo torsion
j	-5022039141376/111166451	j-invariant
L	3.1132991091103	L(r)(E,1)/r!
Ω	1.18073381662	Real period
R	0.32959366722706	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	2992e1 11968k1 13464h1 37400c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1496d1

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	1	-2	+	-4	-	0	-3	-4	5	3	-12	-2	0	2	7	-4	-5	-1	4	14	-10	-1	5

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Quadratic twists for elliptic curve 1496d1

-4	8	-3	5	-7	-11	17
2992e1	11968k1	13464h1	37400c1	73304bb1	16456c1	25432w1

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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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