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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 819.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 819.c1 | 819e3 | \([0, 0, 1, -1056, 32553]\) | \(-178643795968/524596891\) | \(-382431133539\) | \([3]\) | \(864\) | \(0.90941\) | |
| 819.c2 | 819e1 | \([0, 0, 1, -66, -207]\) | \(-43614208/91\) | \(-66339\) | \([]\) | \(96\) | \(-0.18920\) | \(\Gamma_0(N)\)-optimal |
| 819.c3 | 819e2 | \([0, 0, 1, 114, -1026]\) | \(224755712/753571\) | \(-549353259\) | \([3]\) | \(288\) | \(0.36010\) |
Rank
sage: E.rank()
The elliptic curves in class 819.c have rank \(0\).
Complex multiplication
The elliptic curves in class 819.c do not have complex multiplication.Modular form 819.2.a.c
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
