Cremona's table of elliptic curves

2211 = 3 · 11 · 67

Field	Data	Notes
Atkin-Lehner	3+ 11+ 67+	Signs for the Atkin-Lehner involutions
Class	2211a	Isogeny class
Conductor	2211	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	17924577 = 3 · 113 · 672	Discriminant
Eigenvalues	1 3+  0  0 11+  4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-105,-408]	[a1,a2,a3,a4,a6]
Generators	[1142:13097:8]	Generators of the group modulo torsion
j	129938649625/17924577	j-invariant
L	3.2226397286358	L(r)(E,1)/r!
Ω	1.5032195034665	Real period
R	4.2876502349847	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	35376bb1 6633e1 55275k1 108339k1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2211a1

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	0	+	4	2	-2	2	-2	8	-6	-6	-12	-6	4	-6	-4	+	2	-10	8	8	-6	-14

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Quadratic twists for elliptic curve 2211a1

-4	-3	5	-7	-11
35376bb1	6633e1	55275k1	108339k1	24321e1

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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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