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	17745i	Isogeny class
Conductor	17745	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	1172486473175745 = 35 · 5 · 7 · 1310	Discriminant
Eigenvalues	-1 3+ 5- 7-  0 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-39465,-2544690]	[a1,a2,a3,a4,a6]
Generators	[-29050:167427:343]	Generators of the group modulo torsion
j	1408317602329/242911305	j-invariant
L	3.0584701917817	L(r)(E,1)/r!
Ω	0.34271434261264	Real period
R	8.9242550179424	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53235s1 88725bm1 124215cd1 1365a1	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 17745i1

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

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Quadratic twists for elliptic curve 17745i1

-3	5	-7	13
53235s1	88725bm1	124215cd1	1365a1

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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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