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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 333795.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333795.bq1 | 333795bq4 | \([1, 1, 0, -593467, -176219264]\) | \(957681397954009/31185\) | \(752730089265\) | \([2]\) | \(1966080\) | \(1.7802\) | |
| 333795.bq2 | 333795bq3 | \([1, 1, 0, -58817, 801906]\) | \(932288503609/527295615\) | \(12727634290459935\) | \([2]\) | \(1966080\) | \(1.7802\) | |
| 333795.bq3 | 333795bq2 | \([1, 1, 0, -37142, -2757129]\) | \(234770924809/1334025\) | \(32200120485225\) | \([2, 2]\) | \(983040\) | \(1.4336\) | |
| 333795.bq4 | 333795bq1 | \([1, 1, 0, -1017, -91104]\) | \(-4826809/144375\) | \(-3484861524375\) | \([2]\) | \(491520\) | \(1.0871\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333795.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 333795.bq do not have complex multiplication.Modular form 333795.2.a.bq
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.
