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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 10800.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10800.bv1 | 10800db1 | \([0, 0, 0, -16200, -796500]\) | \(-5971968/25\) | \(-1968300000000\) | \([]\) | \(20736\) | \(1.2140\) | \(\Gamma_0(N)\)-optimal |
| 10800.bv2 | 10800db2 | \([0, 0, 0, 37800, -4198500]\) | \(8429568/15625\) | \(-11071687500000000\) | \([]\) | \(62208\) | \(1.7633\) |
Rank
sage: E.rank()
The elliptic curves in class 10800.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 10800.bv do not have complex multiplication.Modular form 10800.2.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 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.
