Cremona's table of elliptic curves

1221 = 3 · 11 · 37

Field	Data	Notes
Atkin-Lehner	3- 11+ 37-	Signs for the Atkin-Lehner involutions
Class	1221a	Isogeny class
Conductor	1221	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	-32967 = -1 · 34 · 11 · 37	Discriminant
Eigenvalues	1 3-  2 -4 11+ -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,5,-7]	[a1,a2,a3,a4,a6]
Generators	[13:41:1]	Generators of the group modulo torsion
j	18191447/32967	j-invariant
L	3.565623445966	L(r)(E,1)/r!
Ω	1.9337022528036	Real period
R	1.8439361286342	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19536y1 78144r1 3663e1 30525d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1221a1

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
1	-	2	-4	+	-6	-2	-4	4	2	-8	-	6	-4	8	-2	0	-6	-12	8	2	-8	4	-2	2

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Quadratic twists for elliptic curve 1221a1

-4	8	-3	5	-7	-11	37
19536y1	78144r1	3663e1	30525d1	59829c1	13431g1	45177e1

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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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