Cremona's table of elliptic curves

1859 = 11 · 13²

Field	Data	Notes
Atkin-Lehner	11- 13+	Signs for the Atkin-Lehner involutions
Class	1859b	Isogeny class
Conductor	1859	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-8973037931 = -1 · 11 · 138	Discriminant
Eigenvalues	0 -1  1  2 11- 13+ -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-225,-4665]	[a1,a2,a3,a4,a6]
j	-262144/1859	j-invariant
L	1.0927167659368	L(r)(E,1)/r!
Ω	0.54635838296838	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	29744m1 118976e1 16731e1 46475c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1859b1

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
0	-1	1	2	-	+	-4	-2	7	-2	3	11	-10	-4	4	2	1	-2	1	9	16	8	0	7	13

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Quadratic twists for elliptic curve 1859b1

-4	8	-3	5	-7	-11	13
29744m1	118976e1	16731e1	46475c1	91091k1	20449b1	143a1

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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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