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	1862a	Isogeny class
Conductor	1862	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	432	Modular degree for the optimal curve
Δ	-182476 = -1 · 22 · 74 · 19	Discriminant
Eigenvalues	2+ -2 -3 7+ -3 -4 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-75,242]	[a1,a2,a3,a4,a6]
Generators	[-10:8:1] [-3:22:1]	Generators of the group modulo torsion
j	-19061833/76	j-invariant
L	1.8268078524335	L(r)(E,1)/r!
Ω	3.2151943597438	Real period
R	0.8522694033558	Regulator
r	2	Rank of the group of rational points
S	0.99999999999947	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	14896x1 59584g1 16758y1 46550bu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1862a1

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
+	-2	-3	+	-3	-4	-6	-	-3	-6	-10	2	-12	-1	-3	6	-6	-7	2	-12	-7	-10	9	0	8

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Quadratic twists for elliptic curve 1862a1

-4	8	-3	5	-7	-19
14896x1	59584g1	16758y1	46550bu1	1862c1	35378j1

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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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