Properties

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

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 44100.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.bc1 44100bw1 \([0, 0, 0, -44776200, 76676749625]\) \(463030539649024/149501953125\) \(3205550650363769531250000\) \([2]\) \(7741440\) \(3.4057\) \(\Gamma_0(N)\)-optimal
44100.bc2 44100bw2 \([0, 0, 0, 127489425, 524050577750]\) \(667990736021936/732392128125\) \(-251257727520865012500000000\) \([2]\) \(15482880\) \(3.7523\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 44100.2.a.bc

sage: E.q_eigenform(10)
 
\(q - 2 q^{11} + 4 q^{13} - 6 q^{17} - 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.