Properties

Label 39600dg
Number of curves $2$
Conductor $39600$
CM no
Rank $1$
Graph

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

Elliptic curves in class 39600dg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39600.dq2 39600dg1 \([0, 0, 0, -17400, 1026875]\) \(-3196715008/649539\) \(-118378482750000\) \([2]\) \(122880\) \(1.4228\) \(\Gamma_0(N)\)-optimal
39600.dq1 39600dg2 \([0, 0, 0, -290775, 60349250]\) \(932410994128/29403\) \(85739148000000\) \([2]\) \(245760\) \(1.7694\)  

Rank

sage: E.rank()
 

The elliptic curves in class 39600dg have rank \(1\).

Complex multiplication

The elliptic curves in class 39600dg do not have complex multiplication.

Modular form 39600.2.a.dg

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} - q^{11} - 6 q^{13} - 4 q^{17} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.