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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 7938.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7938.bc1 | 7938z1 | \([1, -1, 1, -3611, -215477]\) | \(-60698457/200704\) | \(-17213603549184\) | \([]\) | \(27648\) | \(1.2260\) | \(\Gamma_0(N)\)-optimal |
| 7938.bc2 | 7938z2 | \([1, -1, 1, 31669, 5048299]\) | \(505636983/1882384\) | \(-13077026686909584\) | \([]\) | \(82944\) | \(1.7753\) |
Rank
sage: E.rank()
The elliptic curves in class 7938.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 7938.bc do not have complex multiplication.Modular form 7938.2.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.
