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	732c	Isogeny class
Conductor	732	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	711504 = 24 · 36 · 61	Discriminant
Eigenvalues	2- 3- -2 -2  0 -6  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-29,36]	[a1,a2,a3,a4,a6]
Generators	[-5:9:1]	Generators of the group modulo torsion
j	174456832/44469	j-invariant
L	2.2682272677785	L(r)(E,1)/r!
Ω	2.6755394130489	Real period
R	0.18839210571613	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	2928h1 11712g1 2196c1 18300a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 732c1

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	-2	0	-6	0	0	-4	0	-6	-6	6	-2	0	4	0	+	-2	8	6	10	-12	12	2

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Quadratic twists for elliptic curve 732c1

-4	8	-3	5	-7	-11	13	61
2928h1	11712g1	2196c1	18300a1	35868e1	88572d1	123708h1	44652g1

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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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