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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 4800bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4800.e2 | 4800bz1 | \([0, -1, 0, -3208, -81338]\) | \(-29218112/6561\) | \(-820125000000\) | \([2]\) | \(7680\) | \(1.0062\) | \(\Gamma_0(N)\)-optimal |
| 4800.e1 | 4800bz2 | \([0, -1, 0, -53833, -4789463]\) | \(2156689088/81\) | \(648000000000\) | \([2]\) | \(15360\) | \(1.3528\) |
Rank
sage: E.rank()
The elliptic curves in class 4800bz have rank \(1\).
Complex multiplication
The elliptic curves in class 4800bz do not have complex multiplication.Modular form 4800.2.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 Cremona 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 Cremona labels.
