Properties

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

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 44100.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.bd1 44100bu1 \([0, 0, 0, -58800, 2015125]\) \(1048576/525\) \(11256803381250000\) \([2]\) \(221184\) \(1.7728\) \(\Gamma_0(N)\)-optimal
44100.bd2 44100bu2 \([0, 0, 0, 216825, 15520750]\) \(3286064/2205\) \(-756457187220000000\) \([2]\) \(442368\) \(2.1193\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 44100.2.a.bd

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