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	2210a	Isogeny class
Conductor	2210	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	18828492800 = 218 · 52 · 132 · 17	Discriminant
Eigenvalues	2+  2 5- -2 -4 13- 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2227,-40851]	[a1,a2,a3,a4,a6]
Generators	[-27:36:1]	Generators of the group modulo torsion
j	1222331589867961/18828492800	j-invariant
L	3.0777102440435	L(r)(E,1)/r!
Ω	0.69558381636062	Real period
R	2.2123216294382	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	17680n1 70720d1 19890ba1 11050m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2210a1

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

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Quadratic twists for elliptic curve 2210a1

-4	8	-3	5	-7	13	17
17680n1	70720d1	19890ba1	11050m1	108290j1	28730s1	37570c1

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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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