Cremona's table of elliptic curves

4361 = 7² · 89

Field	Data	Notes
Atkin-Lehner	7- 89+	Signs for the Atkin-Lehner involutions
Class	4361b	Isogeny class
Conductor	4361	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	900	Modular degree for the optimal curve
Δ	10470761 = 76 · 89	Discriminant
Eigenvalues	1 -2  2 7- -4 -2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-75,-199]	[a1,a2,a3,a4,a6]
j	389017/89	j-invariant
L	0.82581228501314	L(r)(E,1)/r!
Ω	1.6516245700263	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	69776q1 39249o1 109025h1 89b2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4361b1

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	2	-	-4	-2	-6	2	2	-6	-6	10	6	2	-12	-6	10	6	12	4	-10	-12	6	+	18

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Quadratic twists for elliptic curve 4361b1

-4	-3	5	-7
69776q1	39249o1	109025h1	89b2

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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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