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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 92046bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92046.bm1 | 92046bc1 | \([1, 0, 0, -48679, -4185463]\) | \(-86175179713/1152576\) | \(-170622612800064\) | \([]\) | \(760320\) | \(1.5385\) | \(\Gamma_0(N)\)-optimal |
92046.bm2 | 92046bc2 | \([1, 0, 0, 173501, -21115579]\) | \(3901777377407/3560891556\) | \(-527139747125053284\) | \([]\) | \(2280960\) | \(2.0878\) |
Rank
sage: E.rank()
The elliptic curves in class 92046bc have rank \(0\).
Complex multiplication
The elliptic curves in class 92046bc do not have complex multiplication.Modular form 92046.2.a.bc
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.