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	1496b	Isogeny class
Conductor	1496	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-47872 = -1 · 28 · 11 · 17	Discriminant
Eigenvalues	2+  0  0  3 11+ -4 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-20,36]	[a1,a2,a3,a4,a6]
Generators	[2:2:1]	Generators of the group modulo torsion
j	-3456000/187	j-invariant
L	2.8225218590667	L(r)(E,1)/r!
Ω	3.5328654520725	Real period
R	0.19973318382469	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	2992c1 11968f1 13464s1 37400q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1496b1

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	0	3	+	-4	+	-6	-2	-1	0	6	3	-2	-3	-3	-9	2	-11	14	11	-8	-6	1	-6

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Quadratic twists for elliptic curve 1496b1

-4	8	-3	5	-7	-11	17
2992c1	11968f1	13464s1	37400q1	73304j1	16456k1	25432j1

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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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