Cremona's table of elliptic curves

1540 = 2² · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	1540a	Isogeny class
Conductor	1540	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-67760 = -1 · 24 · 5 · 7 · 112	Discriminant
Eigenvalues	2-  0 5- 7+ 11+  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,8,9]	[a1,a2,a3,a4,a6]
Generators	[0:3:1]	Generators of the group modulo torsion
j	3538944/4235	j-invariant
L	2.8083697985972	L(r)(E,1)/r!
Ω	2.3235731242982	Real period
R	0.80576182983852	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6160q1 24640f1 13860k1 7700g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1540a1

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	-	+	+	2	-6	4	-2	-2	-10	2	-12	0	0	-6	6	0	2	-8	-10	0	4	-6	-2

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Quadratic twists for elliptic curve 1540a1

-4	8	-3	5	-7	-11
6160q1	24640f1	13860k1	7700g1	10780c1	16940g1

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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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