Cremona's table of elliptic curves

220 = 2² · 5 · 11

Field	Data	Notes
Atkin-Lehner	2- 5- 11+	Signs for the Atkin-Lehner involutions
Class	220a	Isogeny class
Conductor	220	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	36	Modular degree for the optimal curve
Δ	242000 = 24 · 53 · 112	Discriminant
Eigenvalues	2- -2 5- -4 11+ -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-45,100]	[a1,a2,a3,a4,a6]
Generators	[-7:11:1]	Generators of the group modulo torsion
j	643956736/15125	j-invariant
L	1.1411181830796	L(r)(E,1)/r!
Ω	3.1205498610519	Real period
R	0.73135712223162	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	880j1 3520g1 1980b1 1100b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 220a1

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
-	-2	-	-4	+	-4	0	-4	-6	-6	8	2	6	8	6	-6	-12	2	-10	-12	-16	8	0	6	14

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Quadratic twists for elliptic curve 220a1

-4	8	-3	5	-7	-11	13	17	-19	-23
880j1	3520g1	1980b1	1100b1	10780f1	2420g1	37180d1	63580d1	79420b1	116380e1

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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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