Properties

Label 260100cu
Number of curves $2$
Conductor $260100$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cu1")
 
E.isogeny_class()
 

Elliptic curves in class 260100cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
260100.cu2 260100cu1 \([0, 0, 0, 758625, 67553750]\) \(27440/17\) \(-29913689261700000000\) \([]\) \(3110400\) \(2.4262\) \(\Gamma_0(N)\)-optimal
260100.cu1 260100cu2 \([0, 0, 0, -12246375, 17091098750]\) \(-115431760/4913\) \(-8645056196631300000000\) \([]\) \(9331200\) \(2.9755\)  

Rank

sage: E.rank()
 

The elliptic curves in class 260100cu have rank \(0\).

Complex multiplication

The elliptic curves in class 260100cu do not have complex multiplication.

Modular form 260100.2.a.cu

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