Cremona's table of elliptic curves

732 = 2² · 3 · 61

Field	Data	Notes
Atkin-Lehner	2- 3+ 61-	Signs for the Atkin-Lehner involutions
Class	732b	Isogeny class
Conductor	732	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-1264896 = -1 · 28 · 34 · 61	Discriminant
Eigenvalues	2- 3+  1 -5  5  1 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-100,424]	[a1,a2,a3,a4,a6]
Generators	[10:-18:1]	Generators of the group modulo torsion
j	-436334416/4941	j-invariant
L	1.9306520941554	L(r)(E,1)/r!
Ω	2.7343523121622	Real period
R	0.11767881834198	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	2928n1 11712i1 2196e1 18300l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 732b1

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	-5	5	1	-6	-2	-7	4	-8	6	-7	-8	-8	-6	3	-	3	-12	13	9	0	0	-10

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Quadratic twists for elliptic curve 732b1

-4	8	-3	5	-7	-11	13	61
2928n1	11712i1	2196e1	18300l1	35868h1	88572a1	123708d1	44652c1

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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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