Cremona's table of elliptic curves

1562 = 2 · 11 · 71

Field	Data	Notes
Atkin-Lehner	2+ 11+ 71+	Signs for the Atkin-Lehner involutions
Class	1562a	Isogeny class
Conductor	1562	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	274912 = 25 · 112 · 71	Discriminant
Eigenvalues	2+  1 -2  3 11+ -5  6 -3	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-17,4]	[a1,a2,a3,a4,a6]
Generators	[-2:6:1]	Generators of the group modulo torsion
j	498677257/274912	j-invariant
L	2.3054583702698	L(r)(E,1)/r!
Ω	2.6859043926879	Real period
R	0.42917729621095	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	12496i1 49984i1 14058h1 39050m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1562a1

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	-2	3	+	-5	6	-3	9	-6	-9	-4	-10	5	7	2	-4	-14	2	+	-11	12	8	-11	-8

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Quadratic twists for elliptic curve 1562a1

-4	8	-3	5	-7	-11	-71
12496i1	49984i1	14058h1	39050m1	76538k1	17182e1	110902d1

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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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