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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 178752bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 178752.hv2 | 178752bq1 | \([0, 1, 0, 48347, -4318693]\) | \(103737344000/127413867\) | \(-15349876775611392\) | \([2]\) | \(1327104\) | \(1.7919\) | \(\Gamma_0(N)\)-optimal |
| 178752.hv1 | 178752bq2 | \([0, 1, 0, -287793, -41764689]\) | \(1367595682000/402300927\) | \(775459664046047232\) | \([2]\) | \(2654208\) | \(2.1385\) |
Rank
sage: E.rank()
The elliptic curves in class 178752bq have rank \(0\).
Complex multiplication
The elliptic curves in class 178752bq do not have complex multiplication.Modular form 178752.2.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 Cremona 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 Cremona labels.
