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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 259182.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259182.z1 | 259182z1 | \([1, -1, 0, -395148, 95312080]\) | \(142653955969251/677915392\) | \(32426148683706624\) | \([2]\) | \(4055040\) | \(2.0174\) | \(\Gamma_0(N)\)-optimal |
| 259182.z2 | 259182z2 | \([1, -1, 0, -191868, 193089760]\) | \(-16330999139811/327112335088\) | \(-15646485297442473936\) | \([2]\) | \(8110080\) | \(2.3640\) |
Rank
sage: E.rank()
The elliptic curves in class 259182.z have rank \(1\).
Complex multiplication
The elliptic curves in class 259182.z do not have complex multiplication.Modular form 259182.2.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.
