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	16	Product of Tamagawa factors cp
Δ	11872927755 = 37 · 5 · 13 · 174	Discriminant
Eigenvalues	1 3- 5- -4  4 13- 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-9414,353893]	[a1,a2,a3,a4,a6]
Generators	[462:-85:8]	Generators of the group modulo torsion
j	126574061279329/16286595	j-invariant
L	5.0613131887144	L(r)(E,1)/r!
Ω	1.2238890307584	Real period
R	4.1354347179483	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	3315b3 49725f4 129285w4	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 9945k3

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 9945k3

-3	5	13
3315b3	49725f4	129285w4

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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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