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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 107100bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
107100.cc1 | 107100bi1 | \([0, 0, 0, -75900, 8040625]\) | \(265327034368/297381\) | \(54197687250000\) | \([2]\) | \(368640\) | \(1.5494\) | \(\Gamma_0(N)\)-optimal |
107100.cc2 | 107100bi2 | \([0, 0, 0, -56775, 12190750]\) | \(-6940769488/18000297\) | \(-52488866052000000\) | \([2]\) | \(737280\) | \(1.8959\) |
Rank
sage: E.rank()
The elliptic curves in class 107100bi have rank \(2\).
Complex multiplication
The elliptic curves in class 107100bi do not have complex multiplication.Modular form 107100.2.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 Cremona 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 Cremona labels.