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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 222180.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
222180.c1 | 222180z1 | \([0, -1, 0, -299061, -62847414]\) | \(1248870793216/42525\) | \(100723618875600\) | \([2]\) | \(1478400\) | \(1.7786\) | \(\Gamma_0(N)\)-optimal |
222180.c2 | 222180z2 | \([0, -1, 0, -285836, -68671704]\) | \(-68150496976/14467005\) | \(-548258802263665920\) | \([2]\) | \(2956800\) | \(2.1252\) |
Rank
sage: E.rank()
The elliptic curves in class 222180.c have rank \(1\).
Complex multiplication
The elliptic curves in class 222180.c do not have complex multiplication.Modular form 222180.2.a.c
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.