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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 5850bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5850.bc2 | 5850bo1 | \([1, -1, 1, -1175, 19887]\) | \(-9836106385/3407872\) | \(-62108467200\) | \([]\) | \(8640\) | \(0.78239\) | \(\Gamma_0(N)\)-optimal |
5850.bc1 | 5850bo2 | \([1, -1, 1, -101975, 12559407]\) | \(-6434774386429585/140608\) | \(-2562580800\) | \([]\) | \(25920\) | \(1.3317\) |
Rank
sage: E.rank()
The elliptic curves in class 5850bo have rank \(1\).
Complex multiplication
The elliptic curves in class 5850bo do not have complex multiplication.Modular form 5850.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.