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	726c	Isogeny class
Conductor	726	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	935384208 = 24 · 3 · 117	Discriminant
Eigenvalues	2+ 3+  2  4 11-  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-244,-128]	[a1,a2,a3,a4,a6]
j	912673/528	j-invariant
L	1.3230677870826	L(r)(E,1)/r!
Ω	1.3230677870826	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	5808bf1 23232cg1 2178k1 18150dc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 726c1

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
+	+	2	4	-	6	-2	-4	4	-6	0	6	6	-4	-12	2	12	14	4	-12	6	4	-4	10	-14

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Quadratic twists for elliptic curve 726c1

-4	8	-3	5	-7	-11	13
5808bf1	23232cg1	2178k1	18150dc1	35574bk1	66b1	122694cq1

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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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