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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 72450bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72450.bu2 | 72450bo1 | \([1, -1, 0, -200292, 46849616]\) | \(-78013216986489/37918720000\) | \(-431917920000000000\) | \([2]\) | \(1032192\) | \(2.0894\) | \(\Gamma_0(N)\)-optimal |
72450.bu1 | 72450bo2 | \([1, -1, 0, -3512292, 2534161616]\) | \(420676324562824569/56350000000\) | \(641861718750000000\) | \([2]\) | \(2064384\) | \(2.4360\) |
Rank
sage: E.rank()
The elliptic curves in class 72450bo have rank \(1\).
Complex multiplication
The elliptic curves in class 72450bo do not have complex multiplication.Modular form 72450.2.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 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.