Properties

Label 236992.bd
Number of curves $2$
Conductor $236992$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 236992.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.bd1 236992bd2 \([0, 0, 0, -8064076, -8786520720]\) \(1494447319737/5411854\) \(210016303324386033664\) \([2]\) \(9732096\) \(2.7605\)  
236992.bd2 236992bd1 \([0, 0, 0, -277196, -261444496]\) \(-60698457/725788\) \(-28165451757789380608\) \([2]\) \(4866048\) \(2.4139\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 236992.bd have rank \(2\).

Complex multiplication

The elliptic curves in class 236992.bd do not have complex multiplication.

Modular form 236992.2.a.bd

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - q^{7} - 3 q^{9} - 4 q^{11} - 4 q^{13} + 8 q^{17} - 2 q^{19} + O(q^{20})\) 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.