Cremona's table of elliptic curves

17745 = 3 · 5 · 7 · 13²

Field	Data	Notes
Atkin-Lehner	3- 5- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	17745t	Isogeny class
Conductor	17745	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	16128	Modular degree for the optimal curve
Δ	-177892045695 = -1 · 34 · 5 · 7 · 137	Discriminant
Eigenvalues	-1 3- 5- 7+  0 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,1095,14832]	[a1,a2,a3,a4,a6]
Generators	[39:3440:27]	Generators of the group modulo torsion
j	30080231/36855	j-invariant
L	4.0354945416495	L(r)(E,1)/r!
Ω	0.67918641648875	Real period
R	5.9416596735137	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	53235h1 88725r1 124215h1 1365e1	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 17745t1

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

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Quadratic twists for elliptic curve 17745t1

-3	5	-7	13
53235h1	88725r1	124215h1	1365e1

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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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