Cremona's table of elliptic curves

1886 = 2 · 23 · 41

Field	Data	Notes
Atkin-Lehner	2+ 23- 41-	Signs for the Atkin-Lehner involutions
Class	1886c	Isogeny class
Conductor	1886	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	9333557504 = 28 · 232 · 413	Discriminant
Eigenvalues	2+  0 -2  2  2 -2  4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1313,18045]	[a1,a2,a3,a4,a6]
Generators	[17:12:1]	Generators of the group modulo torsion
j	250440136856937/9333557504	j-invariant
L	2.0601480766823	L(r)(E,1)/r!
Ω	1.2864975220333	Real period
R	0.5337872897535	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	15088c1 60352h1 16974l1 47150i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1886c1

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	-2	2	2	-2	4	-2	-	2	0	2	-	-8	-12	8	12	-14	2	0	-6	-6	-16	-12	12

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Quadratic twists for elliptic curve 1886c1

-4	8	-3	5	-7	-23	41
15088c1	60352h1	16974l1	47150i1	92414h1	43378e1	77326d1

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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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