Cremona's table of elliptic curves

2210 = 2 · 5 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 5- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	2210f	Isogeny class
Conductor	2210	Conductor
∏ cp	80	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	1838720000 = 210 · 54 · 132 · 17	Discriminant
Eigenvalues	2- -2 5- -2  0 13+ 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-360,1600]	[a1,a2,a3,a4,a6]
Generators	[-10:70:1]	Generators of the group modulo torsion
j	5160676199041/1838720000	j-invariant
L	3.3216287650319	L(r)(E,1)/r!
Ω	1.3609976129575	Real period
R	0.1220291914331	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	17680k1 70720k1 19890f1 11050i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2210f1

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

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Quadratic twists for elliptic curve 2210f1

-4	8	-3	5	-7	13	17
17680k1	70720k1	19890f1	11050i1	108290be1	28730f1	37570h1

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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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