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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 880.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 880.d1 | 880f1 | \([0, -1, 0, -16, -64]\) | \(-117649/440\) | \(-1802240\) | \([]\) | \(96\) | \(-0.11396\) | \(\Gamma_0(N)\)-optimal |
| 880.d2 | 880f2 | \([0, -1, 0, 144, 1600]\) | \(80062991/332750\) | \(-1362944000\) | \([]\) | \(288\) | \(0.43535\) |
Rank
sage: E.rank()
The elliptic curves in class 880.d have rank \(1\).
Complex multiplication
The elliptic curves in class 880.d do not have complex multiplication.Modular form 880.2.a.d
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.
