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	17745d	Isogeny class
Conductor	17745	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1.0046215848112E+20	Discriminant
Eigenvalues	1 3+ 5+ 7+ -4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-23098078,-42734836763]	[a1,a2,a3,a4,a6]
Generators	[-57163872638701270:61066565329027601:20638466407000]	Generators of the group modulo torsion
j	282352188585428161201/20813369346315	j-invariant
L	3.6837928797585	L(r)(E,1)/r!
Ω	0.068866420846657	Real period
R	26.745929543522	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	53235be6 88725bt6 124215cw6 1365b5	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 17745d5

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

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Quadratic twists for elliptic curve 17745d5

-3	5	-7	13
53235be6	88725bt6	124215cw6	1365b5

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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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