Properties

Label 44100.a
Number of curves $2$
Conductor $44100$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 44100.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.a1 44100dt2 \([0, 0, 0, -13377000, -18831557500]\) \(-30866268160/3\) \(-25729836300000000\) \([]\) \(1632960\) \(2.5822\)  
44100.a2 44100dt1 \([0, 0, 0, -147000, -31727500]\) \(-40960/27\) \(-231568526700000000\) \([]\) \(544320\) \(2.0329\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 44100.a have rank \(1\).

Complex multiplication

The elliptic curves in class 44100.a do not have complex multiplication.

Modular form 44100.2.a.a

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