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	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-5271552 = -1 · 212 · 32 · 11 · 13	Discriminant
Eigenvalues	2+ 3+  2  0 11- 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,6,-108]	[a1,a2,a3,a4,a6]
j	18191447/5271552	j-invariant
L	1.1358111271594	L(r)(E,1)/r!
Ω	1.1358111271594	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	6864u1 27456bc1 2574t1 21450cp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 858a1

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 858a1

-4	8	-3	5	-7	-11	13
6864u1	27456bc1	2574t1	21450cp1	42042bt1	9438v1	11154w1

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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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