Properties

Label 254016ba
Number of curves $2$
Conductor $254016$
CM no
Rank $1$
Graph

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

Elliptic curves in class 254016ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254016.ba1 254016ba1 \([0, 0, 0, -19404, 1136016]\) \(-35937/4\) \(-89932296093696\) \([]\) \(663552\) \(1.4149\) \(\Gamma_0(N)\)-optimal
254016.ba2 254016ba2 \([0, 0, 0, 121716, -1629936]\) \(109503/64\) \(-116552255737430016\) \([]\) \(1990656\) \(1.9642\)  

Rank

sage: E.rank()
 

The elliptic curves in class 254016ba have rank \(1\).

Complex multiplication

The elliptic curves in class 254016ba do not have complex multiplication.

Modular form 254016.2.a.ba

sage: E.q_eigenform(10)
 
\(q - 3 q^{5} - q^{13} + 3 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.