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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 338100.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338100.bj1 | 338100bj1 | \([0, -1, 0, -310333, -67321463]\) | \(-280944640/4347\) | \(-51142020300000000\) | \([]\) | \(3732480\) | \(2.0082\) | \(\Gamma_0(N)\)-optimal |
338100.bj2 | 338100bj2 | \([0, -1, 0, 1159667, -331921463]\) | \(14660034560/12519843\) | \(-147294700910700000000\) | \([]\) | \(11197440\) | \(2.5575\) |
Rank
sage: E.rank()
The elliptic curves in class 338100.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 338100.bj do not have complex multiplication.Modular form 338100.2.a.bj
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.