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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 167310.dr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 167310.dr1 | 167310bn1 | \([1, -1, 1, -1553, -63943]\) | \(-117649/440\) | \(-1548247254840\) | \([]\) | \(276480\) | \(1.0247\) | \(\Gamma_0(N)\)-optimal |
| 167310.dr2 | 167310bn2 | \([1, -1, 1, 13657, 1523981]\) | \(80062991/332750\) | \(-1170861986472750\) | \([]\) | \(829440\) | \(1.5740\) |
Rank
sage: E.rank()
The elliptic curves in class 167310.dr have rank \(1\).
Complex multiplication
The elliptic curves in class 167310.dr do not have complex multiplication.Modular form 167310.2.a.dr
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.
