Cremona's table of elliptic curves

244 = 2² · 61

Field	Data	Notes
Atkin-Lehner	2- 61-	Signs for the Atkin-Lehner involutions
Class	244a	Isogeny class
Conductor	244	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	-15616 = -1 · 28 · 61	Discriminant
Eigenvalues	2-  0 -3 -3 -1  1 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1,6]	[a1,a2,a3,a4,a6]
Generators	[-1:2:1]	Generators of the group modulo torsion
j	432/61	j-invariant
L	1.3210444110455	L(r)(E,1)/r!
Ω	3.0228752686121	Real period
R	0.14567195067143	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	976c1 3904a1 2196f1 6100b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 244a1

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	-3	-3	-1	1	-2	2	3	-8	0	-2	-3	8	-4	-10	9	-	13	-12	5	-17	12	-8	-18

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Quadratic twists for elliptic curve 244a1

-4	8	-3	5	-7	-11	13	17	-19	-23	61
976c1	3904a1	2196f1	6100b1	11956b1	29524f1	41236e1	70516c1	88084c1	129076a1	14884c1

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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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