Cremona's table of elliptic curves

9945 = 3² · 5 · 13 · 17

Field	Data	Notes
Atkin-Lehner	3- 5- 13- 17-	Signs for the Atkin-Lehner involutions
Class	9945k	Isogeny class
Conductor	9945	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-663668386875 = -1 · 37 · 54 · 134 · 17	Discriminant
Eigenvalues	1 3- 5- -4  4 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,1656,28975]	[a1,a2,a3,a4,a6]
Generators	[14:227:1]	Generators of the group modulo torsion
j	688699320191/910381875	j-invariant
L	5.0613131887144	L(r)(E,1)/r!
Ω	0.61194451537919	Real period
R	1.0338586794871	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	3315b4 49725f3 129285w3	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 9945k4

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

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Quadratic twists for elliptic curve 9945k4

-3	5	13
3315b4	49725f3	129285w3

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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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