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	10	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	3659337 = 35 · 11 · 372	Discriminant
Eigenvalues	-1 3-  0 -4 11+  4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-68,-201]	[a1,a2,a3,a4,a6]
Generators	[-5:7:1]	Generators of the group modulo torsion
j	34805634625/3659337	j-invariant
L	1.8953848447743	L(r)(E,1)/r!
Ω	1.6737158640586	Real period
R	0.45297649032929	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	19536w1 78144o1 3663d1 30525c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1221b1

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 1221b1

-4	8	-3	5	-7	-11	37
19536w1	78144o1	3663d1	30525c1	59829d1	13431f1	45177d1

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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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