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SageMath
E = EllipticCurve("kb1")
E.isogeny_class()
Elliptic curves in class 433200.kb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
433200.kb1 | 433200kb2 | \([0, 1, 0, -233714408, 1375141243188]\) | \(468898230633769/5540400\) | \(16681791941913600000000\) | \([2]\) | \(79626240\) | \(3.4141\) | \(\Gamma_0(N)\)-optimal* |
433200.kb2 | 433200kb1 | \([0, 1, 0, -14226408, 22656187188]\) | \(-105756712489/12476160\) | \(-37564924076605440000000\) | \([2]\) | \(39813120\) | \(3.0675\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 433200.kb have rank \(0\).
Complex multiplication
The elliptic curves in class 433200.kb do not have complex multiplication.Modular form 433200.2.a.kb
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.