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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 38720bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38720.bb1 | 38720bk1 | \([0, -1, 0, -685505, -220313663]\) | \(-76711450249/851840\) | \(-395597977286082560\) | \([]\) | \(645120\) | \(2.1915\) | \(\Gamma_0(N)\)-optimal |
38720.bb2 | 38720bk2 | \([0, -1, 0, 2295935, -1143963775]\) | \(2882081488391/2883584000\) | \(-1339148194184953856000\) | \([]\) | \(1935360\) | \(2.7408\) |
Rank
sage: E.rank()
The elliptic curves in class 38720bk have rank \(1\).
Complex multiplication
The elliptic curves in class 38720bk do not have complex multiplication.Modular form 38720.2.a.bk
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.