Cremona's table of elliptic curves

858 = 2 · 3 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 13+	Signs for the Atkin-Lehner involutions
Class	858a	Isogeny class
Conductor	858	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	13703976 = 23 · 32 · 114 · 13	Discriminant
Eigenvalues	2+ 3+  2  0 11- 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-4994,-137940]	[a1,a2,a3,a4,a6]
j	13778603383488553/13703976	j-invariant
L	1.1358111271594	L(r)(E,1)/r!
Ω	0.56790556357971	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6864u4 27456bc4 2574t4 21450cp4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858a3

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	0	-	+	2	4	8	-6	-4	-6	-2	8	12	14	12	2	12	4	6	-8	-12	10	2

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Quadratic twists for elliptic curve 858a3

-4	8	-3	5	-7	-11	13
6864u4	27456bc4	2574t4	21450cp4	42042bt4	9438v4	11154w3

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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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