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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 4032.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4032.j1 | 4032d1 | \([0, 0, 0, -216, -1080]\) | \(55296/7\) | \(141087744\) | \([2]\) | \(1536\) | \(0.29296\) | \(\Gamma_0(N)\)-optimal |
| 4032.j2 | 4032d2 | \([0, 0, 0, 324, -5616]\) | \(11664/49\) | \(-15801827328\) | \([2]\) | \(3072\) | \(0.63953\) |
Rank
sage: E.rank()
The elliptic curves in class 4032.j have rank \(0\).
Complex multiplication
The elliptic curves in class 4032.j do not have complex multiplication.Modular form 4032.2.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.
