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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 183456.ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
183456.ce1 | 183456cz2 | \([0, 0, 0, -14700, 241472]\) | \(1000000/507\) | \(178108102029312\) | \([2]\) | \(368640\) | \(1.4269\) | |
183456.ce2 | 183456cz1 | \([0, 0, 0, -8085, -277144]\) | \(10648000/117\) | \(642216714048\) | \([2]\) | \(184320\) | \(1.0804\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 183456.ce have rank \(1\).
Complex multiplication
The elliptic curves in class 183456.ce do not have complex multiplication.Modular form 183456.2.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 LMFDB 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 LMFDB labels.