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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 56784.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56784.bc1 | 56784by2 | \([0, -1, 0, -9935837240, 381205001294064]\) | \(-5486773802537974663600129/2635437714\) | \(-52104210337278468096\) | \([]\) | \(33191424\) | \(4.0222\) | |
| 56784.bc2 | 56784by1 | \([0, -1, 0, 1930600, 11665250544]\) | \(40251338884511/2997011332224\) | \(-59252741207985329012736\) | \([]\) | \(4741632\) | \(3.0492\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 56784.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 56784.bc do not have complex multiplication.Modular form 56784.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
