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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 318402.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 318402.cl1 | 318402cl1 | \([1, -1, 0, -19346238, 55423186132]\) | \(-549754417/592704\) | \(-863341135572277120820544\) | \([]\) | \(47278080\) | \(3.2878\) | \(\Gamma_0(N)\)-optimal |
| 318402.cl2 | 318402cl2 | \([1, -1, 0, 162142902, -1000662119528]\) | \(323648023823/484243284\) | \(-705355703187102992968167924\) | \([]\) | \(141834240\) | \(3.8371\) |
Rank
sage: E.rank()
The elliptic curves in class 318402.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 318402.cl do not have complex multiplication.Modular form 318402.2.a.cl
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
