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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 350064.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350064.bq1 | 350064bq1 | \([0, 0, 0, -12144675, -16289199326]\) | \(66342819962001390625/4812668669952\) | \(14370551645777952768\) | \([2]\) | \(11354112\) | \(2.7271\) | \(\Gamma_0(N)\)-optimal |
| 350064.bq2 | 350064bq2 | \([0, 0, 0, -11361315, -18481510622]\) | \(-54315282059491182625/17983956399469632\) | \(-53699806065513929637888\) | \([2]\) | \(22708224\) | \(3.0737\) |
Rank
sage: E.rank()
The elliptic curves in class 350064.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 350064.bq do not have complex multiplication.Modular form 350064.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
