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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 64400.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64400.ci1 | 64400p2 | \([0, -1, 0, -9408, 155312]\) | \(5756278756/2705927\) | \(43294832000000\) | \([2]\) | \(153600\) | \(1.3109\) | |
64400.ci2 | 64400p1 | \([0, -1, 0, 2092, 17312]\) | \(253012016/181447\) | \(-725788000000\) | \([2]\) | \(76800\) | \(0.96428\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 64400.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 64400.ci do not have complex multiplication.Modular form 64400.2.a.ci
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.