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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 882d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 882.d2 | 882d1 | \([1, -1, 0, -9, 27]\) | \(-2401/6\) | \(-214326\) | \([]\) | \(96\) | \(-0.28917\) | \(\Gamma_0(N)\)-optimal |
| 882.d1 | 882d2 | \([1, -1, 0, -1269, -17739]\) | \(-6329617441/279936\) | \(-9999593856\) | \([]\) | \(672\) | \(0.68378\) |
Rank
sage: E.rank()
The elliptic curves in class 882d have rank \(1\).
Complex multiplication
The elliptic curves in class 882d do not have complex multiplication.Modular form 882.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
