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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 353925dc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
353925.dc2 | 353925dc1 | \([1, -1, 0, 53883, 6064416]\) | \(857375/1287\) | \(-25970613689109375\) | \([2]\) | \(2211840\) | \(1.8350\) | \(\Gamma_0(N)\)-optimal |
353925.dc1 | 353925dc2 | \([1, -1, 0, -354492, 61195041]\) | \(244140625/61347\) | \(1237932585847546875\) | \([2]\) | \(4423680\) | \(2.1816\) |
Rank
sage: E.rank()
The elliptic curves in class 353925dc have rank \(0\).
Complex multiplication
The elliptic curves in class 353925dc do not have complex multiplication.Modular form 353925.2.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 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.