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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 72128.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72128.x1 | 72128bz2 | \([0, -1, 0, -3593, -100127]\) | \(-42592000/12167\) | \(-1465789832192\) | \([]\) | \(69120\) | \(1.0496\) | |
| 72128.x2 | 72128bz1 | \([0, -1, 0, 327, 1009]\) | \(32000/23\) | \(-2770869248\) | \([]\) | \(23040\) | \(0.50026\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72128.x have rank \(0\).
Complex multiplication
The elliptic curves in class 72128.x do not have complex multiplication.Modular form 72128.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
