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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 50960cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50960.cb1 | 50960cd1 | \([0, -1, 0, -659360, -205830400]\) | \(65787589563409/10400000\) | \(5011659161600000\) | \([2]\) | \(552960\) | \(2.0231\) | \(\Gamma_0(N)\)-optimal |
| 50960.cb2 | 50960cd2 | \([0, -1, 0, -596640, -246623488]\) | \(-48743122863889/26406250000\) | \(-12724915840000000000\) | \([2]\) | \(1105920\) | \(2.3696\) |
Rank
sage: E.rank()
The elliptic curves in class 50960cd have rank \(1\).
Complex multiplication
The elliptic curves in class 50960cd do not have complex multiplication.Modular form 50960.2.a.cd
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.
