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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 92400.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.bc1 | 92400fb1 | \([0, -1, 0, -857701208, -9696242819088]\) | \(-43612581618346739773945/147358175518034712\) | \(-235773080828855539200000000\) | \([]\) | \(37324800\) | \(3.9246\) | \(\Gamma_0(N)\)-optimal |
| 92400.bc2 | 92400fb2 | \([0, -1, 0, 1832308792, -50399637059088]\) | \(425206334414152986757655/931885180314516223488\) | \(-1491016288503225957580800000000\) | \([]\) | \(111974400\) | \(4.4739\) |
Rank
sage: E.rank()
The elliptic curves in class 92400.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 92400.bc do not have complex multiplication.Modular form 92400.2.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 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.
