Properties

Label 254320g
Number of curves $2$
Conductor $254320$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 254320g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254320.g1 254320g1 \([0, 1, 0, -60830261, -182631793565]\) \(-251784668965666816/353546875\) \(-34954289520832000000\) \([]\) \(30357504\) \(3.0224\) \(\Gamma_0(N)\)-optimal
254320.g2 254320g2 \([0, 1, 0, -44646261, -281910923165]\) \(-99546392709922816/289614925147075\) \(-28633498579629498206924800\) \([]\) \(91072512\) \(3.5717\)  

Rank

sage: E.rank()
 

The elliptic curves in class 254320g have rank \(0\).

Complex multiplication

The elliptic curves in class 254320g do not have complex multiplication.

Modular form 254320.2.a.g

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{5} + 5 q^{7} + q^{9} - q^{11} - 4 q^{13} + 2 q^{15} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.