Properties

Label 229320.k
Number of curves $2$
Conductor $229320$
CM no
Rank $0$
Graph

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

Elliptic curves in class 229320.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.k1 229320bh1 \([0, 0, 0, -393078, 19143173]\) \(14270199808/7921875\) \(3728703552005250000\) \([2]\) \(3096576\) \(2.2540\) \(\Gamma_0(N)\)-optimal
229320.k2 229320bh2 \([0, 0, 0, 1536297, 151498298]\) \(53247522512/32131125\) \(-241977945710932704000\) \([2]\) \(6193152\) \(2.6005\)  

Rank

sage: E.rank()
 

The elliptic curves in class 229320.k have rank \(0\).

Complex multiplication

The elliptic curves in class 229320.k do not have complex multiplication.

Modular form 229320.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4q^{11} - q^{13} + 2q^{17} + 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.