Cremona's table of elliptic curves

17710 = 2 · 5 · 7 · 11 · 23

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 11- 23+	Signs for the Atkin-Lehner involutions
Class	17710m	Isogeny class
Conductor	17710	Conductor
∏ cp	400	Product of Tamagawa factors cp
deg	70400	Modular degree for the optimal curve
Δ	-27540461132800 = -1 · 210 · 52 · 75 · 112 · 232	Discriminant
Eigenvalues	2- -2 5- 7- 11- -6  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,6055,-175175]	[a1,a2,a3,a4,a6]
Generators	[70:735:1]	Generators of the group modulo torsion
j	24550575200187119/27540461132800	j-invariant
L	5.6095811337523	L(r)(E,1)/r!
Ω	0.35924586844361	Real period
R	0.15614880020904	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	88550m1 123970bg1	Quadratic twists by: 5 -7

Hecke Eigenvalues for elliptic curve 17710m1

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

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Quadratic twists for elliptic curve 17710m1

5	-7
88550m1	123970bg1

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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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