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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 236992.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
236992.bj1 | 236992bj2 | \([0, 0, 0, -15817100, -23994686704]\) | \(926859375/9604\) | \(4534637733004090277888\) | \([2]\) | \(10174464\) | \(2.9725\) | |
236992.bj2 | 236992bj1 | \([0, 0, 0, -243340, -926833392]\) | \(-3375/784\) | \(-370174508816660430848\) | \([2]\) | \(5087232\) | \(2.6260\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236992.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 236992.bj do not have complex multiplication.Modular form 236992.2.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.