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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 368720bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
368720.bi2 | 368720bi1 | \([0, 0, 0, -15470107, -23403530806]\) | \(99964020929586731506161/81651246490000000\) | \(334443505623040000000\) | \([]\) | \(34075776\) | \(2.8673\) | \(\Gamma_0(N)\)-optimal |
368720.bi1 | 368720bi2 | \([0, 0, 0, -1499229307, 22343395853354]\) | \(90984613355465878035683930961/249396782289047639290\) | \(1021529220255939130531840\) | \([]\) | \(238530432\) | \(3.8402\) |
Rank
sage: E.rank()
The elliptic curves in class 368720bi have rank \(0\).
Complex multiplication
The elliptic curves in class 368720bi do not have complex multiplication.Modular form 368720.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.