Properties

Label 7650.ci
Number of curves $4$
Conductor $7650$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ci1")
 
E.isogeny_class()
 

Elliptic curves in class 7650.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7650.ci1 7650by4 \([1, -1, 1, -25430, 1084947]\) \(159661140625/48275138\) \(549883993781250\) \([2]\) \(41472\) \(1.5335\)  
7650.ci2 7650by3 \([1, -1, 1, -23180, 1363947]\) \(120920208625/19652\) \(223848562500\) \([2]\) \(20736\) \(1.1869\)  
7650.ci3 7650by2 \([1, -1, 1, -9680, -364053]\) \(8805624625/2312\) \(26335125000\) \([2]\) \(13824\) \(0.98421\)  
7650.ci4 7650by1 \([1, -1, 1, -680, -4053]\) \(3048625/1088\) \(12393000000\) \([2]\) \(6912\) \(0.63763\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7650.ci have rank \(1\).

Complex multiplication

The elliptic curves in class 7650.ci do not have complex multiplication.

Modular form 7650.2.a.ci

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 4 q^{7} + q^{8} - 6 q^{11} - 2 q^{13} + 4 q^{14} + q^{16} - q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.