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	1221b	Isogeny class
Conductor	1221	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	264362373 = 310 · 112 · 37	Discriminant
Eigenvalues	-1 3-  0 -4 11+  4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-253,1316]	[a1,a2,a3,a4,a6]
Generators	[-13:56:1]	Generators of the group modulo torsion
j	1791399948625/264362373	j-invariant
L	1.8953848447743	L(r)(E,1)/r!
Ω	1.6737158640586	Real period
R	0.22648824516465	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	19536w2 78144o2 3663d2 30525c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1221b2

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	-	0	-4	+	4	2	-2	6	-6	0	-	-6	-10	-12	-14	6	0	-4	0	-6	10	-12	4	18

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Quadratic twists for elliptic curve 1221b2

-4	8	-3	5	-7	-11	37
19536w2	78144o2	3663d2	30525c2	59829d2	13431f2	45177d2

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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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