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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 443760k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.k2 | 443760k1 | \([0, -1, 0, -185516, -3230340]\) | \(235984/135\) | \(403944201593890560\) | \([]\) | \(6241536\) | \(2.0681\) | \(\Gamma_0(N)\)-optimal* |
443760.k1 | 443760k2 | \([0, -1, 0, -9726356, 11678574156]\) | \(34008433744/375\) | \(1122067226649696000\) | \([]\) | \(18724608\) | \(2.6174\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 443760k have rank \(0\).
Complex multiplication
The elliptic curves in class 443760k do not have complex multiplication.Modular form 443760.2.a.k
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.