Cremona's table of elliptic curves

11858 = 2 · 7² · 11²

Field	Data	Notes
Atkin-Lehner	2- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	11858ba	Isogeny class
Conductor	11858	Conductor
∏ cp	108	Product of Tamagawa factors cp
deg	725760	Modular degree for the optimal curve
Δ	57517907388401152 = 29 · 78 · 117	Discriminant
Eigenvalues	2- -3 -4 7+ 11-  1 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3706737,2747757345]	[a1,a2,a3,a4,a6]
Generators	[135:47364:1]	Generators of the group modulo torsion
j	551516475321/5632	j-invariant
L	2.6784071088599	L(r)(E,1)/r!
Ω	0.31862731043501	Real period
R	0.077834087068425	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	94864bn1 106722by1 11858bo1 1078b1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 11858ba1

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
-	-3	-4	+	-	1	-2	-6	-2	-1	4	-2	2	-4	2	-12	9	5	-9	4	2	15	6	6	-5

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Quadratic twists for elliptic curve 11858ba1

-4	-3	-7	-11
94864bn1	106722by1	11858bo1	1078b1

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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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