Properties

Label 229320.ca
Number of curves $2$
Conductor $229320$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.ca1 229320bu1 \([0, 0, 0, -1585983, 767896738]\) \(20093868785104/26374985\) \(579092519650095360\) \([2]\) \(4423680\) \(2.3150\) \(\Gamma_0(N)\)-optimal
229320.ca2 229320bu2 \([0, 0, 0, -1153803, 1195668502]\) \(-1934207124196/5912841025\) \(-519292353335207961600\) \([2]\) \(8847360\) \(2.6616\)  

Rank

sage: E.rank()
 

The elliptic curves in class 229320.ca have rank \(1\).

Complex multiplication

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

Modular form 229320.2.a.ca

sage: E.q_eigenform(10)
 
\(q - q^{5} + 2 q^{11} + q^{13} + 6 q^{17} + 6 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.