Properties

Label 244800.od
Number of curves $2$
Conductor $244800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("od1")
 
E.isogeny_class()
 

Elliptic curves in class 244800.od

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
244800.od1 244800od2 \([0, 0, 0, -95630700, -371557294000]\) \(-32391289681150609/1228250000000\) \(-3667534848000000000000000\) \([]\) \(34836480\) \(3.4835\)  
244800.od2 244800od1 \([0, 0, 0, 5745300, -1645486000]\) \(7023836099951/4456448000\) \(-13306882424832000000000\) \([]\) \(11612160\) \(2.9342\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 244800.od have rank \(1\).

Complex multiplication

The elliptic curves in class 244800.od do not have complex multiplication.

Modular form 244800.2.a.od

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.