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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 23104.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23104.bi1 | 23104n2 | \([0, 1, 0, -5953, 175135]\) | \(-246579625/512\) | \(-48452599808\) | \([]\) | \(20736\) | \(0.93613\) | |
23104.bi2 | 23104n1 | \([0, 1, 0, 127, 1247]\) | \(2375/8\) | \(-757071872\) | \([]\) | \(6912\) | \(0.38682\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23104.bi have rank \(2\).
Complex multiplication
The elliptic curves in class 23104.bi do not have complex multiplication.Modular form 23104.2.a.bi
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.