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	1710g	Isogeny class
Conductor	1710	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	6215946512400 = 24 · 316 · 52 · 192	Discriminant
Eigenvalues	2+ 3- 5+  4  0 -6 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-277020,-56050304]	[a1,a2,a3,a4,a6]
Generators	[627:3743:1]	Generators of the group modulo torsion
j	3225005357698077121/8526675600	j-invariant
L	2.2323440489626	L(r)(E,1)/r!
Ω	0.20809985080627	Real period
R	5.3636368318226	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	13680bd2 54720bx2 570i2 8550bh2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710g2

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

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Quadratic twists for elliptic curve 1710g2

-4	8	-3	5	-7	-19
13680bd2	54720bx2	570i2	8550bh2	83790bs2	32490bo2

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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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