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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 11088.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11088.f1 | 11088m2 | \([0, 0, 0, -205131, 25081450]\) | \(1278763167594532/375974556419\) | \(280663502468557824\) | \([2]\) | \(92160\) | \(2.0538\) | |
| 11088.f2 | 11088m1 | \([0, 0, 0, 34449, 2608846]\) | \(24226243449392/29774625727\) | \(-5556659751675648\) | \([2]\) | \(46080\) | \(1.7073\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11088.f have rank \(0\).
Complex multiplication
The elliptic curves in class 11088.f do not have complex multiplication.Modular form 11088.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
