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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 55545.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55545.f1 | 55545m4 | \([1, 0, 0, -2343481, 1376328380]\) | \(9614816895690721/34652610405\) | \(5129829987474825045\) | \([2]\) | \(1081344\) | \(2.4513\) | |
| 55545.f2 | 55545m2 | \([1, 0, 0, -214256, -428505]\) | \(7347774183121/4251692025\) | \(629403008675085225\) | \([2, 2]\) | \(540672\) | \(2.1048\) | |
| 55545.f3 | 55545m1 | \([1, 0, 0, -148131, -21892680]\) | \(2428257525121/8150625\) | \(1206585017780625\) | \([2]\) | \(270336\) | \(1.7582\) | \(\Gamma_0(N)\)-optimal |
| 55545.f4 | 55545m3 | \([1, 0, 0, 856969, -3213690]\) | \(470166844956479/272118787605\) | \(-40283346636708355845\) | \([2]\) | \(1081344\) | \(2.4513\) |
Rank
sage: E.rank()
The elliptic curves in class 55545.f have rank \(0\).
Complex multiplication
The elliptic curves in class 55545.f do not have complex multiplication.Modular form 55545.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
