Properties

Label 912.k
Number of curves $4$
Conductor $912$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 912.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
912.k1 912k3 \([0, 1, 0, -1400832, 637689780]\) \(74220219816682217473/16416\) \(67239936\) \([2]\) \(5760\) \(1.7946\)  
912.k2 912k2 \([0, 1, 0, -87552, 9941940]\) \(18120364883707393/269485056\) \(1103810789376\) \([2, 2]\) \(2880\) \(1.4480\)  
912.k3 912k4 \([0, 1, 0, -84992, 10553268]\) \(-16576888679672833/2216253521952\) \(-9077774425915392\) \([4]\) \(5760\) \(1.7946\)  
912.k4 912k1 \([0, 1, 0, -5632, 144308]\) \(4824238966273/537919488\) \(2203318222848\) \([2]\) \(1440\) \(1.1014\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 912.k have rank \(0\).

Complex multiplication

The elliptic curves in class 912.k do not have complex multiplication.

Modular form 912.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2q^{5} + q^{9} + 4q^{11} + 2q^{13} + 2q^{15} - 6q^{17} + q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.