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
Δ	-413160699392 = -1 · 29 · 76 · 193	Discriminant
Eigenvalues	2+ -1  0 7- -6 -5 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,465,-30491]	[a1,a2,a3,a4,a6]
j	94196375/3511808	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	14896bd2 59584bg2 16758bc2 46550ca2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1862b2

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 1862b2

-4	8	-3	5	-7	-19
14896bd2	59584bg2	16758bc2	46550ca2	38a1	35378o2

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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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