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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 388815.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388815.bb1 | 388815bb3 | \([1, 0, 0, -130927511, 576606190656]\) | \(14251520160844849/264449745\) | \(4605729298796988684945\) | \([2]\) | \(48660480\) | \(3.2817\) | |
| 388815.bb2 | 388815bb2 | \([1, 0, 0, -8450786, 8387672691]\) | \(3832302404449/472410225\) | \(8227626063068344626225\) | \([2, 2]\) | \(24330240\) | \(2.9352\) | |
| 388815.bb3 | 388815bb1 | \([1, 0, 0, -2100141, -1035414360]\) | \(58818484369/7455105\) | \(129840153652286275905\) | \([2]\) | \(12165120\) | \(2.5886\) | \(\Gamma_0(N)\)-optimal |
| 388815.bb4 | 388815bb4 | \([1, 0, 0, 12415619, 43272128570]\) | \(12152722588271/53476250625\) | \(-931357049685842116850625\) | \([2]\) | \(48660480\) | \(3.2817\) |
Rank
sage: E.rank()
The elliptic curves in class 388815.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 388815.bb do not have complex multiplication.Modular form 388815.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
