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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 141267.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141267.bk1 | 141267bp2 | \([0, -1, 1, -42960864, 108483510449]\) | \(-1713910976512/1594323\) | \(-8157006238846372305363\) | \([]\) | \(15446340\) | \(3.1273\) | |
141267.bk2 | 141267bp1 | \([0, -1, 1, -109874, -15196231]\) | \(-28672/3\) | \(-15348846323197443\) | \([]\) | \(1188180\) | \(1.8449\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141267.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 141267.bk do not have complex multiplication.Modular form 141267.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.