Properties

Label 238260e
Number of curves $4$
Conductor $238260$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 238260e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
238260.e4 238260e1 \([0, -1, 0, 78939, 31339386]\) \(72268906496/606436875\) \(-456485712884190000\) \([2]\) \(2052864\) \(2.0699\) \(\Gamma_0(N)\)-optimal
238260.e3 238260e2 \([0, -1, 0, -1139436, 431453736]\) \(13584145739344/1195803675\) \(14401955172713644800\) \([2]\) \(4105728\) \(2.4165\)  
238260.e2 238260e3 \([0, -1, 0, -5639301, 5160457710]\) \(-26348629355659264/24169921875\) \(-18193524292968750000\) \([2]\) \(6158592\) \(2.6192\)  
238260.e1 238260e4 \([0, -1, 0, -90248676, 330026613960]\) \(6749703004355978704/5671875\) \(68310619212000000\) \([2]\) \(12317184\) \(2.9658\)  

Rank

sage: E.rank()
 

The elliptic curves in class 238260e have rank \(0\).

Complex multiplication

The elliptic curves in class 238260e do not have complex multiplication.

Modular form 238260.2.a.e

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.