Cremona's table of elliptic curves

1770 = 2 · 3 · 5 · 59

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 59-	Signs for the Atkin-Lehner involutions
Class	1770c	Isogeny class
Conductor	1770	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	6720	Modular degree for the optimal curve
Δ	-185308378300800 = -1 · 27 · 34 · 52 · 595	Discriminant
Eigenvalues	2+ 3- 5+  1 -5 -3  1  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1104,655006]	[a1,a2,a3,a4,a6]
Generators	[-82:483:1]	Generators of the group modulo torsion
j	-148615915769209/185308378300800	j-invariant
L	2.4360330896836	L(r)(E,1)/r!
Ω	0.45816405400896	Real period
R	0.13292362573887	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	14160m1 56640j1 5310p1 8850w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1770c1

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
+	-	+	1	-5	-3	1	6	0	-6	-2	-3	-11	-9	0	4	-	10	-4	-5	2	-7	-3	-12	-8

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Quadratic twists for elliptic curve 1770c1

-4	8	-3	5	-7	-59
14160m1	56640j1	5310p1	8850w1	86730q1	104430ba1

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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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