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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 471510.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
471510.bo1 | 471510bo2 | \([1, -1, 0, -332258679, -2331026111907]\) | \(1152829477932246539641/3188367360\) | \(11219047755776040960\) | \([2]\) | \(76677120\) | \(3.3135\) | \(\Gamma_0(N)\)-optimal* |
471510.bo2 | 471510bo1 | \([1, -1, 0, -20757879, -36448918947]\) | \(-281115640967896441/468084326400\) | \(-1647068803141887590400\) | \([2]\) | \(38338560\) | \(2.9669\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 471510.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 471510.bo do not have complex multiplication.Modular form 471510.2.a.bo
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.