Properties

Label 230640.b
Number of curves $2$
Conductor $230640$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 230640.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
230640.b1 230640b2 \([0, -1, 0, -25616, -2358720]\) \(-472270995409/341718750\) \(-1345092480000000\) \([]\) \(987840\) \(1.6026\)  
230640.b2 230640b1 \([0, -1, 0, -816, 10176]\) \(-15284209/1920\) \(-7557611520\) \([]\) \(141120\) \(0.62964\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 230640.b have rank \(1\).

Complex multiplication

The elliptic curves in class 230640.b do not have complex multiplication.

Modular form 230640.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 4 q^{7} + q^{9} - 3 q^{11} + 2 q^{13} + q^{15} - 3 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.