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	1740c	Isogeny class
Conductor	1740	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-111360 = -1 · 28 · 3 · 5 · 29	Discriminant
Eigenvalues	2- 3+ 5- -2  3 -2 -4  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5,-15]	[a1,a2,a3,a4,a6]
j	-65536/435	j-invariant
L	1.3978161004426	L(r)(E,1)/r!
Ω	1.3978161004426	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6960bm1 27840bj1 5220g1 8700n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1740c1

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	3	-2	-4	6	-1	-	4	3	3	1	2	-1	4	4	10	6	1	-4	17	6	-13

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Quadratic twists for elliptic curve 1740c1

-4	8	-3	5	-7	29
6960bm1	27840bj1	5220g1	8700n1	85260u1	50460p1

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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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