Cremona's table of elliptic curves

1885 = 5 · 13 · 29

Field	Data	Notes
Atkin-Lehner	5+ 13+ 29+	Signs for the Atkin-Lehner involutions
Class	1885b	Isogeny class
Conductor	1885	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1867663890625 = -1 · 56 · 132 · 294	Discriminant
Eigenvalues	-1  2 5+  0  2 13+ -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-28466,1837888]	[a1,a2,a3,a4,a6]
Generators	[86:144:1]	Generators of the group modulo torsion
j	-2550962067330021409/1867663890625	j-invariant
L	2.504198624561	L(r)(E,1)/r!
Ω	0.8264081814817	Real period
R	1.5151100150479	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30160q2 120640bq2 16965o2 9425e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1885b2

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	2	+	0	2	+	-6	2	-6	+	-2	-2	2	6	4	10	-6	2	-8	-14	-6	8	4	-6	-18

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Quadratic twists for elliptic curve 1885b2

-4	8	-3	5	-7	13	29
30160q2	120640bq2	16965o2	9425e2	92365m2	24505d2	54665d2

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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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