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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 129360.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129360.bj1 | 129360el1 | \([0, -1, 0, -3916096, -2981391104]\) | \(13782741913468081/701662500\) | \(338124355430400000\) | \([2]\) | \(3317760\) | \(2.4335\) | \(\Gamma_0(N)\)-optimal |
129360.bj2 | 129360el2 | \([0, -1, 0, -3704416, -3318216320]\) | \(-11666347147400401/3126621093750\) | \(-1506688389360000000000\) | \([2]\) | \(6635520\) | \(2.7801\) |
Rank
sage: E.rank()
The elliptic curves in class 129360.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 129360.bj do not have complex multiplication.Modular form 129360.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.