Properties

Label 72600co
Number of curves $2$
Conductor $72600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("co1")
 
E.isogeny_class()
 

Elliptic curves in class 72600co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72600.bq1 72600co1 \([0, -1, 0, -25208, -447588]\) \(62500/33\) \(935384208000000\) \([2]\) \(276480\) \(1.5642\) \(\Gamma_0(N)\)-optimal
72600.bq2 72600co2 \([0, -1, 0, 95792, -3593588]\) \(1714750/1089\) \(-61735357728000000\) \([2]\) \(552960\) \(1.9108\)  

Rank

sage: E.rank()
 

The elliptic curves in class 72600co have rank \(1\).

Complex multiplication

The elliptic curves in class 72600co do not have complex multiplication.

Modular form 72600.2.a.co

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