Properties

Label 400064.bd
Number of curves $2$
Conductor $400064$
CM no
Rank $0$
Graph

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

Elliptic curves in class 400064.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
400064.bd1 400064bd1 \([0, 0, 0, -20684, 1138800]\) \(3733252610697/23278724\) \(6102377824256\) \([2]\) \(645120\) \(1.2911\) \(\Gamma_0(N)\)-optimal
400064.bd2 400064bd2 \([0, 0, 0, -8524, 2466672]\) \(-261284780457/9875692358\) \(-2588853497495552\) \([2]\) \(1290240\) \(1.6377\)  

Rank

sage: E.rank()
 

The elliptic curves in class 400064.bd have rank \(0\).

Complex multiplication

The elliptic curves in class 400064.bd do not have complex multiplication.

Modular form 400064.2.a.bd

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} + q^{7} - 3 q^{9} + 2 q^{11} + 6 q^{13} + 2 q^{17} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.