Show commands:
SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 291018.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 291018.bl1 | 291018bl4 | \([1, 0, 1, -231785025, -1358258240012]\) | \(285311789321435384726737/594905980032\) | \(2871497538572277888\) | \([2]\) | \(43352064\) | \(3.2182\) | |
| 291018.bl2 | 291018bl3 | \([1, 0, 1, -18709825, -7856671756]\) | \(150062694782364873937/81319429594096512\) | \(392513354639651390990208\) | \([2]\) | \(43352064\) | \(3.2182\) | |
| 291018.bl3 | 291018bl2 | \([1, 0, 1, -14491585, -21208245004]\) | \(69728644177980628177/100579396829184\) | \(485477537829676793856\) | \([2, 2]\) | \(21676032\) | \(2.8716\) | |
| 291018.bl4 | 291018bl1 | \([1, 0, 1, -647105, -524591884]\) | \(-6208503067778257/21032186413056\) | \(-101518346668216418304\) | \([2]\) | \(10838016\) | \(2.5251\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 291018.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 291018.bl do not have complex multiplication.Modular form 291018.2.a.bl
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
