Cremona's table of elliptic curves

726 = 2 · 3 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3- 11-	Signs for the Atkin-Lehner involutions
Class	726d	Isogeny class
Conductor	726	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-39204 = -1 · 22 · 34 · 112	Discriminant
Eigenvalues	2+ 3- -1 -4 11-  5 -7  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-14,20]	[a1,a2,a3,a4,a6]
Generators	[3:-5:1]	Generators of the group modulo torsion
j	-2259169/324	j-invariant
L	1.7815333278583	L(r)(E,1)/r!
Ω	3.5176356019611	Real period
R	0.063307201535637	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	5808q1 23232m1 2178j1 18150cd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 726d1

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	-4	-	5	-7	0	0	-7	-8	-5	-11	8	4	-5	0	2	12	-16	6	-4	8	-17	-5

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Quadratic twists for elliptic curve 726d1

-4	8	-3	5	-7	-11	13
5808q1	23232m1	2178j1	18150cd1	35574l1	726i1	122694cz1

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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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