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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 4032.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4032.x1 | 4032m1 | \([0, 0, 0, -75, 236]\) | \(1000000/63\) | \(2939328\) | \([2]\) | \(512\) | \(-0.0078109\) | \(\Gamma_0(N)\)-optimal |
| 4032.x2 | 4032m2 | \([0, 0, 0, 60, 992]\) | \(8000/147\) | \(-438939648\) | \([2]\) | \(1024\) | \(0.33876\) |
Rank
sage: E.rank()
The elliptic curves in class 4032.x have rank \(1\).
Complex multiplication
The elliptic curves in class 4032.x do not have complex multiplication.Modular form 4032.2.a.x
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.
