Properties

Label 65088dg
Number of curves $2$
Conductor $65088$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dg1")
 
E.isogeny_class()
 

Elliptic curves in class 65088dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
65088.bo2 65088dg1 \([0, 0, 0, -956748, 362678416]\) \(-506814405937489/4048994304\) \(-773774861301448704\) \([]\) \(774144\) \(2.2605\) \(\Gamma_0(N)\)-optimal
65088.bo1 65088dg2 \([0, 0, 0, -4101708, -35483575664]\) \(-39934705050538129/2823126576537804\) \(-539507890401066120904704\) \([]\) \(5419008\) \(3.2335\)  

Rank

sage: E.rank()
 

The elliptic curves in class 65088dg have rank \(1\).

Complex multiplication

The elliptic curves in class 65088dg do not have complex multiplication.

Modular form 65088.2.a.dg

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