Cremona's table of elliptic curves

64 = 2⁶

Field	Data	Notes
Atkin-Lehner	2-	Signs for the Atkin-Lehner involutions
Class	64a	Isogeny class
Conductor	64	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	32768 = 215	Discriminant
Eigenvalues	2-  0  2  0  0 -6  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-44,-112]	[a1,a2,a3,a4,a6]
j	287496	j-invariant
L	0.92703733865069	L(r)(E,1)/r!
Ω	1.8540746773014	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	64a3 32a3 576h4 1600o3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 64a2

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 64a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
64a3	32a3	576h4	1600o3	3136t4	7744t4	10816bb3	18496i3	23104bo4	33856ba4	53824r4	61504bn4	87616z3	107584h3	118336bd4

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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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