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	17745x	Isogeny class
Conductor	17745	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	174470525775 = 33 · 52 · 76 · 133	Discriminant
Eigenvalues	1 3- 5- 7-  6 13- -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1408,-3157]	[a1,a2,a3,a4,a6]
Generators	[-11:110:1]	Generators of the group modulo torsion
j	140364780373/79413075	j-invariant
L	8.3712985627184	L(r)(E,1)/r!
Ω	0.8404868067764	Real period
R	0.55333663612994	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	53235y2 88725m2 124215t2 17745p2	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 17745x2

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

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Quadratic twists for elliptic curve 17745x2

-3	5	-7	13
53235y2	88725m2	124215t2	17745p2

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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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