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	17745j	Isogeny class
Conductor	17745	Conductor
∏ cp	25	Product of Tamagawa factors cp
deg	14400	Modular degree for the optimal curve
Δ	-26628590625 = -1 · 3 · 55 · 75 · 132	Discriminant
Eigenvalues	-1 3+ 5- 7- -3 13+  8  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-335,-8338]	[a1,a2,a3,a4,a6]
Generators	[32:106:1]	Generators of the group modulo torsion
j	-24606647689/157565625	j-invariant
L	2.8444635627686	L(r)(E,1)/r!
Ω	0.49744653551839	Real period
R	0.22872516820763	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	53235t1 88725bn1 124215ce1 17745c1	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 17745j1

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	+	-	-	-3	+	8	1	-6	-6	1	4	1	-4	9	6	-10	6	-3	9	-6	-14	4	-11	-13

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Quadratic twists for elliptic curve 17745j1

-3	5	-7	13
53235t1	88725bn1	124215ce1	17745c1

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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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