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	732a	Isogeny class
Conductor	732	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-8573184 = -1 · 28 · 32 · 612	Discriminant
Eigenvalues	2- 3+  2  2  2 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,28,120]	[a1,a2,a3,a4,a6]
j	9148592/33489	j-invariant
L	1.6498948210379	L(r)(E,1)/r!
Ω	1.6498948210379	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	2928m2 11712o2 2196d2 18300h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 732a2

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

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Quadratic twists for elliptic curve 732a2

-4	8	-3	5	-7	-11	13	61
2928m2	11712o2	2196d2	18300h2	35868j2	88572b2	123708b2	44652d2

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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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