Properties

Label 142912.bd
Number of curves $2$
Conductor $142912$
CM no
Rank $1$
Graph

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

Elliptic curves in class 142912.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
142912.bd1 142912o2 \([0, 0, 0, -112300, 14227152]\) \(597479568890625/12199182688\) \(3197942546563072\) \([2]\) \(491520\) \(1.7658\)  
142912.bd2 142912o1 \([0, 0, 0, 340, 665296]\) \(16581375/729422848\) \(-191213823066112\) \([2]\) \(245760\) \(1.4193\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 142912.bd have rank \(1\).

Complex multiplication

The elliptic curves in class 142912.bd do not have complex multiplication.

Modular form 142912.2.a.bd

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