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	1710l	Isogeny class
Conductor	1710	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	2052086594400 = 25 · 39 · 52 · 194	Discriminant
Eigenvalues	2- 3+ 5+ -2  2 -4 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3593,-45143]	[a1,a2,a3,a4,a6]
Generators	[-37:208:1]	Generators of the group modulo torsion
j	260549802603/104256800	j-invariant
L	3.7679679235694	L(r)(E,1)/r!
Ω	0.63837041981322	Real period
R	0.29512394423538	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	13680v2 54720i2 1710b2 8550c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710l2

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 1710l2

-4	8	-3	5	-7	-19
13680v2	54720i2	1710b2	8550c2	83790dd2	32490c2

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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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