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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 141610ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141610.q2 | 141610ce1 | \([1, -1, 0, -53230, -4929324]\) | \(-2014698447/108800\) | \(-900775454969600\) | \([2]\) | \(1032192\) | \(1.6281\) | \(\Gamma_0(N)\)-optimal |
141610.q1 | 141610ce2 | \([1, -1, 0, -862430, -308055644]\) | \(8568561392847/23120\) | \(191414784181040\) | \([2]\) | \(2064384\) | \(1.9747\) |
Rank
sage: E.rank()
The elliptic curves in class 141610ce have rank \(0\).
Complex multiplication
The elliptic curves in class 141610ce do not have complex multiplication.Modular form 141610.2.a.ce
sage: E.q_eigenform(10)
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.