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	1740a	Isogeny class
Conductor	1740	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	587250000 = 24 · 34 · 56 · 29	Discriminant
Eigenvalues	2- 3+ 5+  0 -6  6  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-741,-7434]	[a1,a2,a3,a4,a6]
Generators	[-15:9:1]	Generators of the group modulo torsion
j	2816075628544/36703125	j-invariant
L	2.3739981115824	L(r)(E,1)/r!
Ω	0.91566925142619	Real period
R	0.86421238086597	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	6960bg1 27840bw1 5220o1 8700m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1740a1

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	-6	6	4	2	-8	-	-2	0	-2	0	0	-14	4	6	-12	-12	-16	-2	12	-2	-12

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Quadratic twists for elliptic curve 1740a1

-4	8	-3	5	-7	29
6960bg1	27840bw1	5220o1	8700m1	85260bc1	50460j1

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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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