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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 235950.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235950.bc1 | 235950bc2 | \([1, 1, 0, -35294250, -80711662500]\) | \(175654575624148921/21954418200\) | \(607712360325159375000\) | \([2]\) | \(22118400\) | \(3.0107\) | |
235950.bc2 | 235950bc1 | \([1, 1, 0, -2019250, -1483887500]\) | \(-32894113444921/15289560000\) | \(-423224815674375000000\) | \([2]\) | \(11059200\) | \(2.6641\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235950.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 235950.bc do not have complex multiplication.Modular form 235950.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.