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	726i	Isogeny class
Conductor	726	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1056	Modular degree for the optimal curve
Δ	-69452277444 = -1 · 22 · 34 · 118	Discriminant
Eigenvalues	2- 3- -1  4 11- -5  7  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1636,-28588]	[a1,a2,a3,a4,a6]
j	-2259169/324	j-invariant
L	2.9790280848548	L(r)(E,1)/r!
Ω	0.37237851060685	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5808r1 23232l1 2178d1 18150n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 726i1

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 726i1

-4	8	-3	5	-7	-11	13
5808r1	23232l1	2178d1	18150n1	35574cb1	726d1	122694bg1

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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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