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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 4950.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4950.bc1 | 4950bh2 | \([1, -1, 1, -1336505, 595042247]\) | \(-23178622194826561/1610510\) | \(-18344715468750\) | \([]\) | \(72000\) | \(1.9991\) | |
| 4950.bc2 | 4950bh1 | \([1, -1, 1, 2245, 164747]\) | \(109902239/1100000\) | \(-12529687500000\) | \([]\) | \(14400\) | \(1.1944\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4950.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 4950.bc do not have complex multiplication.Modular form 4950.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
