Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 271440bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271440.bb1 | 271440bb1 | \([0, 0, 0, -141348, 20454203]\) | \(26775969499365376/3817125\) | \(44522946000\) | \([2]\) | \(663552\) | \(1.4531\) | \(\Gamma_0(N)\)-optimal |
| 271440.bb2 | 271440bb2 | \([0, 0, 0, -140943, 20577242]\) | \(-1659154206306256/19986890625\) | \(-3730033476000000\) | \([2]\) | \(1327104\) | \(1.7996\) |
Rank
sage: E.rank()
The elliptic curves in class 271440bb have rank \(1\).
Complex multiplication
The elliptic curves in class 271440bb do not have complex multiplication.Modular form 271440.2.a.bb
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.
