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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 17136.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17136.f1 | 17136g3 | \([0, 0, 0, -19731, -1066574]\) | \(569001644066/122451\) | \(182818363392\) | \([2]\) | \(24576\) | \(1.1557\) | |
| 17136.f2 | 17136g4 | \([0, 0, 0, -8931, 315394]\) | \(52767497666/1753941\) | \(2618619881472\) | \([2]\) | \(24576\) | \(1.1557\) | |
| 17136.f3 | 17136g2 | \([0, 0, 0, -1371, -12710]\) | \(381775972/127449\) | \(95140168704\) | \([2, 2]\) | \(12288\) | \(0.80915\) | |
| 17136.f4 | 17136g1 | \([0, 0, 0, 249, -1370]\) | \(9148592/9639\) | \(-1798868736\) | \([2]\) | \(6144\) | \(0.46258\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17136.f have rank \(1\).
Complex multiplication
The elliptic curves in class 17136.f do not have complex multiplication.Modular form 17136.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
