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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 1350.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1350.p1 | 1350n1 | \([1, -1, 1, -380, 3997]\) | \(-19683/10\) | \(-3075468750\) | \([]\) | \(864\) | \(0.52534\) | \(\Gamma_0(N)\)-optimal |
| 1350.p2 | 1350n2 | \([1, -1, 1, 2995, -50003]\) | \(1073733/1000\) | \(-2767921875000\) | \([]\) | \(2592\) | \(1.0746\) |
Rank
sage: E.rank()
The elliptic curves in class 1350.p have rank \(0\).
Complex multiplication
The elliptic curves in class 1350.p do not have complex multiplication.Modular form 1350.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
