Properties

Label 463680.ba
Number of curves $2$
Conductor $463680$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 463680.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.ba1 463680ba1 \([0, 0, 0, -734508, -237686832]\) \(8493409990827/185150000\) \(955333332172800000\) \([2]\) \(5898240\) \(2.2383\) \(\Gamma_0(N)\)-optimal
463680.ba2 463680ba2 \([0, 0, 0, 60372, -725107248]\) \(4716275733/44023437500\) \(-227151267840000000000\) \([2]\) \(11796480\) \(2.5849\)  

Rank

sage: E.rank()
 

The elliptic curves in class 463680.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 463680.ba do not have complex multiplication.

Modular form 463680.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 2q^{11} - 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})\)  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.