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	726a	Isogeny class
Conductor	726	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	2299968 = 26 · 33 · 113	Discriminant
Eigenvalues	2+ 3+  0  0 11+ -6  6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-35,-51]	[a1,a2,a3,a4,a6]
Generators	[-5:8:1]	Generators of the group modulo torsion
j	3723875/1728	j-invariant
L	1.4899240841974	L(r)(E,1)/r!
Ω	2.0448157422174	Real period
R	0.72863488549914	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5808z1 23232bf1 2178h1 18150co1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 726a1

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
+	+	0	0	+	-6	6	-6	6	-6	4	-2	-6	-6	6	-12	-12	-6	4	-6	12	-12	0	-6	-10

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Quadratic twists for elliptic curve 726a1

-4	8	-3	5	-7	-11	13
5808z1	23232bf1	2178h1	18150co1	35574v1	726f1	122694br1

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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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