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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 97020.dc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97020.dc1 | 97020de2 | \([0, 0, 0, -99687, -12114466]\) | \(1711503051568/7425\) | \(475289337600\) | \([2]\) | \(258048\) | \(1.4474\) | |
97020.dc2 | 97020de1 | \([0, 0, 0, -6132, -195559]\) | \(-6373654528/441045\) | \(-1764511665840\) | \([2]\) | \(129024\) | \(1.1008\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 97020.dc have rank \(0\).
Complex multiplication
The elliptic curves in class 97020.dc do not have complex multiplication.Modular form 97020.2.a.dc
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.