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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 55488.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55488.bz1 | 55488u2 | \([0, -1, 0, -2406773889, -45445761389439]\) | \(-843137281012581793/216\) | \(-394989039060516864\) | \([]\) | \(22208256\) | \(3.6589\) | |
| 55488.bz2 | 55488u1 | \([0, -1, 0, -29667969, -62530585983]\) | \(-1579268174113/10077696\) | \(-18428608606407474806784\) | \([]\) | \(7402752\) | \(3.1096\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 55488.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 55488.bz do not have complex multiplication.Modular form 55488.2.a.bz
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.
