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	1862c	Isogeny class
Conductor	1862	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3024	Modular degree for the optimal curve
Δ	-21468118924 = -1 · 22 · 710 · 19	Discriminant
Eigenvalues	2+  2  3 7- -3  4  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3651,-86743]	[a1,a2,a3,a4,a6]
j	-19061833/76	j-invariant
L	2.4560514990298	L(r)(E,1)/r!
Ω	0.30700643737872	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14896bf1 59584bo1 16758bh1 46550cd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1862c1

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 1862c1

-4	8	-3	5	-7	-19
14896bf1	59584bo1	16758bh1	46550cd1	1862a1	35378q1

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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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