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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 73920.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.j1 | 73920dx1 | \([0, -1, 0, -481, -3839]\) | \(188183524/3465\) | \(227082240\) | \([2]\) | \(36864\) | \(0.39803\) | \(\Gamma_0(N)\)-optimal |
| 73920.j2 | 73920dx2 | \([0, -1, 0, -1, -11615]\) | \(-2/444675\) | \(-58284441600\) | \([2]\) | \(73728\) | \(0.74460\) |
Rank
sage: E.rank()
The elliptic curves in class 73920.j have rank \(0\).
Complex multiplication
The elliptic curves in class 73920.j do not have complex multiplication.Modular form 73920.2.a.j
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.
