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
Δ	-176569632000 = -1 · 28 · 38 · 53 · 292	Discriminant
Eigenvalues	2- 3+ 5+  0 -6  6  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-116,-20184]	[a1,a2,a3,a4,a6]
Generators	[58:406:1]	Generators of the group modulo torsion
j	-680136784/689725125	j-invariant
L	2.3739981115824	L(r)(E,1)/r!
Ω	0.45783462571309	Real period
R	1.7284247617319	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	6960bg2 27840bw2 5220o2 8700m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1740a2

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 1740a2

-4	8	-3	5	-7	29
6960bg2	27840bw2	5220o2	8700m2	85260bc2	50460j2

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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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