Cremona's table of elliptic curves

1410 = 2 · 3 · 5 · 47

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 47+	Signs for the Atkin-Lehner involutions
Class	1410f	Isogeny class
Conductor	1410	Conductor
∏ cp	70	Product of Tamagawa factors cp
deg	1120	Modular degree for the optimal curve
Δ	-5139450000 = -1 · 24 · 37 · 55 · 47	Discriminant
Eigenvalues	2+ 3- 5- -3 -6  1  3  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-123,3478]	[a1,a2,a3,a4,a6]
Generators	[59:-480:1]	Generators of the group modulo torsion
j	-203401212841/5139450000	j-invariant
L	2.3348028818414	L(r)(E,1)/r!
Ω	1.1413004711457	Real period
R	0.029224842823351	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11280q1 45120c1 4230bc1 7050w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1410f1

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
+	-	-	-3	-6	1	3	3	-3	-3	-8	-4	-5	-6	+	-1	-13	5	4	-3	10	-10	-8	-10	8

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Quadratic twists for elliptic curve 1410f1

-4	8	-3	5	-7	-47
11280q1	45120c1	4230bc1	7050w1	69090i1	66270j1

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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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