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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 38088.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38088.c1 | 38088o2 | \([0, 0, 0, -8211, -280370]\) | \(3370318/81\) | \(1471383926784\) | \([2]\) | \(73728\) | \(1.1194\) | |
| 38088.c2 | 38088o1 | \([0, 0, 0, 69, -13754]\) | \(4/9\) | \(-81743551488\) | \([2]\) | \(36864\) | \(0.77286\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38088.c have rank \(1\).
Complex multiplication
The elliptic curves in class 38088.c do not have complex multiplication.Modular form 38088.2.a.c
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.
