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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 16800bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16800.bu1 | 16800bv1 | \([0, 1, 0, -658, 6188]\) | \(31554496/525\) | \(525000000\) | \([2]\) | \(9216\) | \(0.47173\) | \(\Gamma_0(N)\)-optimal |
| 16800.bu2 | 16800bv2 | \([0, 1, 0, -33, 18063]\) | \(-64/2205\) | \(-141120000000\) | \([2]\) | \(18432\) | \(0.81830\) |
Rank
sage: E.rank()
The elliptic curves in class 16800bv have rank \(0\).
Complex multiplication
The elliptic curves in class 16800bv do not have complex multiplication.Modular form 16800.2.a.bv
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.
