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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 183872.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
183872.ci1 | 183872bh1 | \([0, -1, 0, -643777, -198580383]\) | \(23320116793/2873\) | \(3635261540139008\) | \([2]\) | \(2064384\) | \(2.0092\) | \(\Gamma_0(N)\)-optimal |
183872.ci2 | 183872bh2 | \([0, -1, 0, -589697, -233375455]\) | \(-17923019113/8254129\) | \(-10444106404819369984\) | \([2]\) | \(4128768\) | \(2.3558\) |
Rank
sage: E.rank()
The elliptic curves in class 183872.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 183872.ci do not have complex multiplication.Modular form 183872.2.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.