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SageMath
E = EllipticCurve("kj1")
E.isogeny_class()
Elliptic curves in class 141120kj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.pv2 | 141120kj1 | \([0, 0, 0, -105987, -13243916]\) | \(69934528/225\) | \(423616024843200\) | \([2]\) | \(917504\) | \(1.6728\) | \(\Gamma_0(N)\)-optimal |
141120.pv1 | 141120kj2 | \([0, 0, 0, -152292, -537824]\) | \(3241792/1875\) | \(225928546583040000\) | \([2]\) | \(1835008\) | \(2.0194\) |
Rank
sage: E.rank()
The elliptic curves in class 141120kj have rank \(0\).
Complex multiplication
The elliptic curves in class 141120kj do not have complex multiplication.Modular form 141120.2.a.kj
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.