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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 296208.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296208.bt1 | 296208bt3 | \([0, 0, 0, -24467600091, 1473109987427210]\) | \(306234591284035366263793/1727485056\) | \(9138141662208701497344\) | \([2]\) | \(247726080\) | \(4.2837\) | |
| 296208.bt2 | 296208bt2 | \([0, 0, 0, -1529252571, 23016472255370]\) | \(74768347616680342513/5615307472896\) | \(29704149964109904561045504\) | \([2, 2]\) | \(123863040\) | \(3.9371\) | |
| 296208.bt3 | 296208bt4 | \([0, 0, 0, -1428890331, 26167906808714]\) | \(-60992553706117024753/20624795251201152\) | \(-109102130930112907607655579648\) | \([2]\) | \(247726080\) | \(4.2837\) | |
| 296208.bt4 | 296208bt1 | \([0, 0, 0, -101878491, 309519915914]\) | \(22106889268753393/4969545596928\) | \(26288164695726066889654272\) | \([2]\) | \(61931520\) | \(3.5905\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 296208.bt have rank \(1\).
Complex multiplication
The elliptic curves in class 296208.bt do not have complex multiplication.Modular form 296208.2.a.bt
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.
