Cremona's table of elliptic curves

1406 = 2 · 19 · 37

Field	Data	Notes
Atkin-Lehner	2- 19- 37+	Signs for the Atkin-Lehner involutions
Class	1406g	Isogeny class
Conductor	1406	Conductor
∏ cp	150	Product of Tamagawa factors cp
deg	7200	Modular degree for the optimal curve
Δ	-111076295671808 = -1 · 215 · 195 · 372	Discriminant
Eigenvalues	2- -3 -2 -1  0  3  5 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1191,507615]	[a1,a2,a3,a4,a6]
Generators	[13:-710:1]	Generators of the group modulo torsion
j	-186688297520577/111076295671808	j-invariant
L	2.3123537740931	L(r)(E,1)/r!
Ω	0.48010055608067	Real period
R	0.032109298004431	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	11248f1 44992n1 12654f1 35150l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1406g1

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	-2	-1	0	3	5	-	-3	-9	-4	+	6	-8	-4	1	3	-8	-7	-6	9	-6	0	14	4

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Quadratic twists for elliptic curve 1406g1

-4	8	-3	5	-7	-19	37
11248f1	44992n1	12654f1	35150l1	68894o1	26714k1	52022e1

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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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