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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1183a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1183.a2 | 1183a1 | \([0, 1, 1, -1239, 16410]\) | \(-43614208/91\) | \(-439239619\) | \([]\) | \(672\) | \(0.54397\) | \(\Gamma_0(N)\)-optimal |
| 1183.a3 | 1183a2 | \([0, 1, 1, 2141, 84179]\) | \(224755712/753571\) | \(-3637343284939\) | \([]\) | \(2016\) | \(1.0933\) | |
| 1183.a1 | 1183a3 | \([0, 1, 1, -19829, -2655480]\) | \(-178643795968/524596891\) | \(-2532128994850819\) | \([]\) | \(6048\) | \(1.6426\) |
Rank
sage: E.rank()
The elliptic curves in class 1183a have rank \(1\).
Complex multiplication
The elliptic curves in class 1183a do not have complex multiplication.Modular form 1183.2.a.a
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
