Cremona's table of elliptic curves

1862 = 2 · 7² · 19

Field	Data	Notes
Atkin-Lehner	2+ 7- 19+	Signs for the Atkin-Lehner involutions
Class	1862b	Isogeny class
Conductor	1862	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	756	Modular degree for the optimal curve
Δ	-17882648 = -1 · 23 · 76 · 19	Discriminant
Eigenvalues	2+ -1  0 7- -6 -5 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-760,-8392]	[a1,a2,a3,a4,a6]
j	-413493625/152	j-invariant
L	0.45455056676453	L(r)(E,1)/r!
Ω	0.45455056676453	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14896bd1 59584bg1 16758bc1 46550ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1862b1

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	0	-	-6	-5	-3	+	3	9	4	2	0	8	0	-3	-9	10	5	-6	7	-10	6	12	10

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Quadratic twists for elliptic curve 1862b1

-4	8	-3	5	-7	-19
14896bd1	59584bg1	16758bc1	46550ca1	38a3	35378o1

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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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