Properties

Label 255024cp
Number of curves $2$
Conductor $255024$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cp1")
 
E.isogeny_class()
 

Elliptic curves in class 255024cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
255024.cp2 255024cp1 \([0, 0, 0, -558435, 160806242]\) \(-6449916994998625/8532911772\) \(-25479138024603648\) \([2]\) \(2064384\) \(2.0545\) \(\Gamma_0(N)\)-optimal
255024.cp1 255024cp2 \([0, 0, 0, -8937795, 10284748994]\) \(26444015547214434625/46191222\) \(137926249832448\) \([2]\) \(4128768\) \(2.4010\)  

Rank

sage: E.rank()
 

The elliptic curves in class 255024cp have rank \(1\).

Complex multiplication

The elliptic curves in class 255024cp do not have complex multiplication.

Modular form 255024.2.a.cp

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