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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 30960.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30960.bq1 | 30960bv3 | \([0, 0, 0, -810147, -280670686]\) | \(-19693718244927649/167968750\) | \(-501552000000000\) | \([]\) | \(373248\) | \(1.9891\) | |
| 30960.bq2 | 30960bv2 | \([0, 0, 0, -5187, -755134]\) | \(-5168743489/79507000\) | \(-237406629888000\) | \([]\) | \(124416\) | \(1.4398\) | |
| 30960.bq3 | 30960bv1 | \([0, 0, 0, 573, 27074]\) | \(6967871/110080\) | \(-328697118720\) | \([]\) | \(41472\) | \(0.89046\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30960.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 30960.bq do not have complex multiplication.Modular form 30960.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
