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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 27200ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27200.bc2 | 27200ci1 | \([0, -1, 0, 638367, 60731137]\) | \(7023836099951/4456448000\) | \(-18253611008000000000\) | \([]\) | \(387072\) | \(2.3849\) | \(\Gamma_0(N)\)-optimal |
| 27200.bc1 | 27200ci2 | \([0, -1, 0, -10625633, 13764923137]\) | \(-32391289681150609/1228250000000\) | \(-5030912000000000000000\) | \([]\) | \(1161216\) | \(2.9342\) |
Rank
sage: E.rank()
The elliptic curves in class 27200ci have rank \(1\).
Complex multiplication
The elliptic curves in class 27200ci do not have complex multiplication.Modular form 27200.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
