Cremona's table of elliptic curves

2220 = 2² · 3 · 5 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 37+	Signs for the Atkin-Lehner involutions
Class	2220b	Isogeny class
Conductor	2220	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	2427570000 = 24 · 38 · 54 · 37	Discriminant
Eigenvalues	2- 3+ 5+  4 -4  2  2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7681,-256550]	[a1,a2,a3,a4,a6]
j	3132662187311104/151723125	j-invariant
L	1.5298995557495	L(r)(E,1)/r!
Ω	0.50996651858316	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8880y1 35520bm1 6660d1 11100l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2220b1

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

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Quadratic twists for elliptic curve 2220b1

-4	8	-3	5	-7	37
8880y1	35520bm1	6660d1	11100l1	108780bp1	82140f1

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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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