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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 34914f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34914.b4 | 34914f1 | \([1, 1, 0, -36776, 4925760]\) | \(-37159393753/49741824\) | \(-7363575136321536\) | \([2]\) | \(202752\) | \(1.7373\) | \(\Gamma_0(N)\)-optimal |
| 34914.b3 | 34914f2 | \([1, 1, 0, -713896, 231760960]\) | \(271808161065433/147476736\) | \(21831849720578304\) | \([2, 2]\) | \(405504\) | \(2.0839\) | |
| 34914.b2 | 34914f3 | \([1, 1, 0, -840856, 143472976]\) | \(444142553850073/196663299888\) | \(29113226432593680432\) | \([2]\) | \(811008\) | \(2.4305\) | |
| 34914.b1 | 34914f4 | \([1, 1, 0, -11420856, 14851044144]\) | \(1112891236915770073/327888\) | \(48539191572432\) | \([2]\) | \(811008\) | \(2.4305\) |
Rank
sage: E.rank()
The elliptic curves in class 34914f have rank \(0\).
Complex multiplication
The elliptic curves in class 34914f do not have complex multiplication.Modular form 34914.2.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 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.
