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	1710d	Isogeny class
Conductor	1710	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-89754480 = -1 · 24 · 310 · 5 · 19	Discriminant
Eigenvalues	2+ 3- 5+  4  4 -2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-90,-540]	[a1,a2,a3,a4,a6]
j	-111284641/123120	j-invariant
L	1.4848404110562	L(r)(E,1)/r!
Ω	0.7424202055281	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13680bh1 54720co1 570m1 8550ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710d1

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
+	-	+	4	4	-2	2	+	8	-6	4	-10	2	12	0	-6	0	-10	-4	8	2	-12	8	-6	18

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Quadratic twists for elliptic curve 1710d1

-4	8	-3	5	-7	-19
13680bh1	54720co1	570m1	8550ba1	83790ck1	32490bp1

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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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