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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 8550z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8550.u2 | 8550z1 | \([1, -1, 1, -5, -4003]\) | \(-1/608\) | \(-6925500000\) | \([]\) | \(4800\) | \(0.56709\) | \(\Gamma_0(N)\)-optimal |
| 8550.u1 | 8550z2 | \([1, -1, 1, -15755, 846497]\) | \(-37966934881/4952198\) | \(-56408630343750\) | \([]\) | \(24000\) | \(1.3718\) |
Rank
sage: E.rank()
The elliptic curves in class 8550z have rank \(1\).
Complex multiplication
The elliptic curves in class 8550z do not have complex multiplication.Modular form 8550.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
