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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 370300bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
370300.bi2 | 370300bi1 | \([0, -1, 0, 14107, 592382]\) | \(1048576/1127\) | \(-333672893806000\) | \([2]\) | \(1520640\) | \(1.4734\) | \(\Gamma_0(N)\)-optimal |
370300.bi1 | 370300bi2 | \([0, -1, 0, -78468, 5591432]\) | \(11279504/3703\) | \(17541660702944000\) | \([2]\) | \(3041280\) | \(1.8200\) |
Rank
sage: E.rank()
The elliptic curves in class 370300bi have rank \(1\).
Complex multiplication
The elliptic curves in class 370300bi do not have complex multiplication.Modular form 370300.2.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.