Properties

Label 44100.e
Number of curves $2$
Conductor $44100$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 44100.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.e1 44100cq2 \([0, 0, 0, -535080, -150652460]\) \(-30866268160/3\) \(-1646709523200\) \([]\) \(326592\) \(1.7775\)  
44100.e2 44100cq1 \([0, 0, 0, -5880, -253820]\) \(-40960/27\) \(-14820385708800\) \([]\) \(108864\) \(1.2282\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 44100.e have rank \(0\).

Complex multiplication

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

Modular form 44100.2.a.e

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.