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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 276606.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
276606.bo1 | 276606bo2 | \([1, -1, 1, -24351244457, -1462608304702927]\) | \(1236526859255318155975783969/38367061931916216\) | \(49549831549709051755685304\) | \([]\) | \(246301440\) | \(4.4347\) | |
276606.bo2 | 276606bo1 | \([1, -1, 1, -111019217, 446019850433]\) | \(117174888570509216929/1273887851544576\) | \(1645185356368047079686144\) | \([]\) | \(35185920\) | \(3.4618\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 276606.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 276606.bo do not have complex multiplication.Modular form 276606.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.