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	32	Product of Tamagawa factors cp
Δ	892373210723255625 = 36 · 54 · 74 · 138	Discriminant
Eigenvalues	1 3+ 5+ 7+ -4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-502778,129263607]	[a1,a2,a3,a4,a6]
Generators	[200390:5950343:1000]	Generators of the group modulo torsion
j	2912015927948401/184878500625	j-invariant
L	3.6837928797585	L(r)(E,1)/r!
Ω	0.27546568338663	Real period
R	6.6864823858805	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	53235be2 88725bt2 124215cw2 1365b2	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 17745d2

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 17745d2

-3	5	-7	13
53235be2	88725bt2	124215cw2	1365b2

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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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