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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 430950.dt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.dt1 | 430950dt2 | \([1, 0, 1, -125376, 17075398]\) | \(6349095794413/520200\) | \(17857490625000\) | \([2]\) | \(2433024\) | \(1.5875\) | \(\Gamma_0(N)\)-optimal* |
430950.dt2 | 430950dt1 | \([1, 0, 1, -8376, 227398]\) | \(1892819053/440640\) | \(15126345000000\) | \([2]\) | \(1216512\) | \(1.2409\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 430950.dt have rank \(1\).
Complex multiplication
The elliptic curves in class 430950.dt do not have complex multiplication.Modular form 430950.2.a.dt
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.