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	1406f	Isogeny class
Conductor	1406	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	224	Modular degree for the optimal curve
Δ	-3329408 = -1 · 27 · 19 · 372	Discriminant
Eigenvalues	2-  1 -2 -1  0 -5 -7 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-19,-95]	[a1,a2,a3,a4,a6]
Generators	[18:65:1]	Generators of the group modulo torsion
j	-761048497/3329408	j-invariant
L	3.8352309354513	L(r)(E,1)/r!
Ω	1.0386418485092	Real period
R	0.26375315727086	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	11248d1 44992k1 12654g1 35150k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1406f1

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
-	1	-2	-1	0	-5	-7	-	1	-1	4	+	-2	0	12	-3	11	0	5	-6	-15	-14	0	6	12

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Quadratic twists for elliptic curve 1406f1

-4	8	-3	5	-7	-19	37
11248d1	44992k1	12654g1	35150k1	68894n1	26714i1	52022c1

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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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