Cremona's table of elliptic curves

1710 = 2 · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 19-	Signs for the Atkin-Lehner involutions
Class	1710b	Isogeny class
Conductor	1710	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	2814933600 = 25 · 33 · 52 · 194	Discriminant
Eigenvalues	2+ 3+ 5- -2 -2 -4  6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-399,1805]	[a1,a2,a3,a4,a6]
Generators	[-19:57:1]	Generators of the group modulo torsion
j	260549802603/104256800	j-invariant
L	2.1762892416983	L(r)(E,1)/r!
Ω	1.3011095265311	Real period
R	0.41816026962396	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	13680x2 54720b2 1710l2 8550u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710b2

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	6	-	8	-6	-8	-8	-12	0	0	10	-6	-6	12	12	-10	-8	-8	-8	-14

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Quadratic twists for elliptic curve 1710b2

-4	8	-3	5	-7	-19
13680x2	54720b2	1710l2	8550u2	83790d2	32490bg2

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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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