Cremona's table of elliptic curves

32 = 2⁵

Field	Data	Notes
Atkin-Lehner	2-	Signs for the Atkin-Lehner involutions
Class	32a	Isogeny class
Conductor	32	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1	Modular degree for the optimal curve
Δ	-4096 = -1 · 212	Discriminant
Eigenvalues	2-  0 -2  0  0  6  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,4,0]	[a1,a2,a3,a4,a6]
j	1728	j-invariant
L	0.65551438857303	L(r)(E,1)/r!
Ω	2.6220575542921	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	32a1 64a4 288d4 800a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 32a1

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
-	0	-2	0	0	6	2	0	0	-10	0	-2	10	0	0	14	0	-10	0	0	-6	0	0	10	18

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Quadratic twists for elliptic curve 32a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59	61
32a1	64a4	288d4	800a4	1568g4	3872b4	5408a4	9248e4	11552h4	16928e4	26912a2	30752f2	43808a2	53792e2	59168e2	70688c2	89888a2	111392b2	119072c2

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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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