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
Δ	25719552 = 28 · 33 · 612	Discriminant
Eigenvalues	2- 3- -2 -2  0 -6  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-164,-828]	[a1,a2,a3,a4,a6]
Generators	[-8:6:1]	Generators of the group modulo torsion
j	1917170512/100467	j-invariant
L	2.2682272677785	L(r)(E,1)/r!
Ω	1.3377697065244	Real period
R	0.37678421143226	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	2928h2 11712g2 2196c2 18300a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 732c2

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 732c2

-4	8	-3	5	-7	-11	13	61
2928h2	11712g2	2196c2	18300a2	35868e2	88572d2	123708h2	44652g2

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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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