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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 479808.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
479808.bc1 | 479808bc2 | \([0, 0, 0, -4746924, -3982822704]\) | \(-19486825371/11662\) | \(-7079335450051608576\) | \([]\) | \(13271040\) | \(2.5610\) | |
479808.bc2 | 479808bc1 | \([0, 0, 0, 51156, -22594096]\) | \(17779581/275128\) | \(-229100858885799936\) | \([]\) | \(4423680\) | \(2.0117\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 479808.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 479808.bc do not have complex multiplication.Modular form 479808.2.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.