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	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	79056 = 24 · 34 · 61	Discriminant
Eigenvalues	2- 3+  2  2  2 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-17,30]	[a1,a2,a3,a4,a6]
j	35995648/4941	j-invariant
L	1.6498948210379	L(r)(E,1)/r!
Ω	3.2997896420758	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	2928m1 11712o1 2196d1 18300h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 732a1

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 732a1

-4	8	-3	5	-7	-11	13	61
2928m1	11712o1	2196d1	18300h1	35868j1	88572b1	123708b1	44652d1

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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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