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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 145200cl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145200.iu1 | 145200cl1 | \([0, 1, 0, -45173, 3861603]\) | \(-56197120/3267\) | \(-592659434188800\) | \([]\) | \(622080\) | \(1.5909\) | \(\Gamma_0(N)\)-optimal |
145200.iu2 | 145200cl2 | \([0, 1, 0, 245227, 6939843]\) | \(8990228480/5314683\) | \(-964125197328691200\) | \([]\) | \(1866240\) | \(2.1402\) |
Rank
sage: E.rank()
The elliptic curves in class 145200cl have rank \(0\).
Complex multiplication
The elliptic curves in class 145200cl do not have complex multiplication.Modular form 145200.2.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 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.