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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 303600.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 303600.z1 | 303600z2 | \([0, -1, 0, -495208, 133252912]\) | \(209849322390625/1882056627\) | \(120451624128000000\) | \([2]\) | \(2949120\) | \(2.1004\) | |
| 303600.z2 | 303600z1 | \([0, -1, 0, -9208, 4948912]\) | \(-1349232625/164333367\) | \(-10517335488000000\) | \([2]\) | \(1474560\) | \(1.7538\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303600.z have rank \(1\).
Complex multiplication
The elliptic curves in class 303600.z do not have complex multiplication.Modular form 303600.2.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 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.
