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	17745c	Isogeny class
Conductor	17745	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	187200	Modular degree for the optimal curve
Δ	-128531120886065625 = -1 · 3 · 55 · 75 · 138	Discriminant
Eigenvalues	1 3+ 5+ 7+  3 13+  8 -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-56618,-18035103]	[a1,a2,a3,a4,a6]
Generators	[31436696:1089244719:24389]	Generators of the group modulo torsion
j	-24606647689/157565625	j-invariant
L	4.3914189024183	L(r)(E,1)/r!
Ω	0.13796684543181	Real period
R	10.609841054383	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	53235bd1 88725bs1 124215cu1 17745j1	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 17745c1

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 17745c1

-3	5	-7	13
53235bd1	88725bs1	124215cu1	17745j1

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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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