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	1710s	Isogeny class
Conductor	1710	Conductor
∏ cp	224	Product of Tamagawa factors cp
Δ	2297811651559833600 = 214 · 316 · 52 · 194	Discriminant
Eigenvalues	2- 3- 5-  4  0  2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-704192,215615459]	[a1,a2,a3,a4,a6]
j	52974743974734147769/3152005008998400	j-invariant
L	3.5691849063025	L(r)(E,1)/r!
Ω	0.2549417790216	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	13680bx2 54720bl2 570d2 8550h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1710s2

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	2	2	+	0	-10	0	2	-2	-4	0	6	-8	6	12	0	-14	0	12	-10	2

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Quadratic twists for elliptic curve 1710s2

-4	8	-3	5	-7	-19
13680bx2	54720bl2	570d2	8550h2	83790ed2	32490z2

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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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