Cremona's table of elliptic curves

1740 = 2² · 3 · 5 · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 29+	Signs for the Atkin-Lehner involutions
Class	1740b	Isogeny class
Conductor	1740	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	5449680 = 24 · 34 · 5 · 292	Discriminant
Eigenvalues	2- 3+ 5-  2 -4  2 -8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-125,570]	[a1,a2,a3,a4,a6]
Generators	[2:18:1]	Generators of the group modulo torsion
j	13608288256/340605	j-invariant
L	2.7042236344182	L(r)(E,1)/r!
Ω	2.4055227062041	Real period
R	1.1241729822145	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	6960bj1 27840bp1 5220j1 8700l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1740b1

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
-	+	-	2	-4	2	-8	-4	-6	+	0	4	6	0	0	-2	0	-6	2	-8	-4	-16	-10	6	8

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Quadratic twists for elliptic curve 1740b1

-4	8	-3	5	-7	29
6960bj1	27840bp1	5220j1	8700l1	85260p1	50460n1

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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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