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Properties

Label 224400.k
Number of curves $2$
Conductor $224400$
CM no
Rank $0$
Graph

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

Elliptic curves in class 224400.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
224400.k1 224400de2 \([0, -1, 0, -24208, 406912]\) \(196122941/104907\) \(839256000000000\) \([2]\) \(1105920\) \(1.5549\)  
224400.k2 224400de1 \([0, -1, 0, 5792, 46912]\) \(2685619/1683\) \(-13464000000000\) \([2]\) \(552960\) \(1.2083\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 224400.k have rank \(0\).

Complex multiplication

The elliptic curves in class 224400.k do not have complex multiplication.

Modular form 224400.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} - q^{11} + 2 q^{13} + q^{17} + 6 q^{19} + O(q^{20})\) Copy content 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.