Cremona's table of elliptic curves

728 = 2³ · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 7+ 13-	Signs for the Atkin-Lehner involutions
Class	728c	Isogeny class
Conductor	728	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-3937024 = -1 · 28 · 7 · 133	Discriminant
Eigenvalues	2-  0 -1 7+  2 13-  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-68,-236]	[a1,a2,a3,a4,a6]
Generators	[12:26:1]	Generators of the group modulo torsion
j	-135834624/15379	j-invariant
L	2.0890611620256	L(r)(E,1)/r!
Ω	0.82600624329523	Real period
R	0.42151843665081	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	1456d1 5824a1 6552g1 18200d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 728c1

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	-1	+	2	-	0	-7	-3	-9	5	-8	-10	5	7	3	0	6	-10	4	-11	-11	11	-3	-15

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Quadratic twists for elliptic curve 728c1

-4	8	-3	5	-7	-11	13
1456d1	5824a1	6552g1	18200d1	5096h1	88088j1	9464c1

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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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