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	726g	Isogeny class
Conductor	726	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-1214383104 = -1 · 210 · 34 · 114	Discriminant
Eigenvalues	2- 3+ -1 -4 11-  3 -1 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,179,1475]	[a1,a2,a3,a4,a6]
Generators	[17:-108:1]	Generators of the group modulo torsion
j	43307231/82944	j-invariant
L	2.489135770989	L(r)(E,1)/r!
Ω	1.0589008370722	Real period
R	0.039177980345972	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	5808bc1 23232bv1 2178e1 18150bh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 726g1

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	-	3	-1	-8	-8	-9	0	3	3	-8	12	11	0	-2	4	0	-6	-4	16	7	-5

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Quadratic twists for elliptic curve 726g1

-4	8	-3	5	-7	-11	13
5808bc1	23232bv1	2178e1	18150bh1	35574da1	726b1	122694s1

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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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