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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 23520.bq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23520.bq1 | 23520t1 | \([0, 1, 0, -30, 48]\) | \(140608/15\) | \(329280\) | \([2]\) | \(2560\) | \(-0.20691\) | \(\Gamma_0(N)\)-optimal |
23520.bq2 | 23520t2 | \([0, 1, 0, 40, 300]\) | \(39304/225\) | \(-39513600\) | \([2]\) | \(5120\) | \(0.13966\) |
Rank
sage: E.rank()
The elliptic curves in class 23520.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 23520.bq do not have complex multiplication.Modular form 23520.2.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.