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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 176610q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176610.de3 | 176610q1 | \([1, 0, 0, -2961, -39399]\) | \(4826809/1680\) | \(999303179280\) | \([2]\) | \(358400\) | \(1.0041\) | \(\Gamma_0(N)\)-optimal |
| 176610.de2 | 176610q2 | \([1, 0, 0, -19781, 1040445]\) | \(1439069689/44100\) | \(26231708456100\) | \([2, 2]\) | \(716800\) | \(1.3507\) | |
| 176610.de1 | 176610q3 | \([1, 0, 0, -314131, 67740155]\) | \(5763259856089/5670\) | \(3372648230070\) | \([2]\) | \(1433600\) | \(1.6972\) | |
| 176610.de4 | 176610q4 | \([1, 0, 0, 5449, 3518031]\) | \(30080231/9003750\) | \(-5355640476453750\) | \([2]\) | \(1433600\) | \(1.6972\) |
Rank
sage: E.rank()
The elliptic curves in class 176610q have rank \(1\).
Complex multiplication
The elliptic curves in class 176610q do not have complex multiplication.Modular form 176610.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
