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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 35322.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35322.f1 | 35322j4 | \([1, 1, 0, -4871930, -2651266776]\) | \(21500025903924625/7344878367708\) | \(4368904943021131718268\) | \([2]\) | \(2419200\) | \(2.8544\) | |
| 35322.f2 | 35322j2 | \([1, 1, 0, -1995710, 1084155828]\) | \(1477843225692625/274663872\) | \(163376476501758912\) | \([2]\) | \(806400\) | \(2.3051\) | |
| 35322.f3 | 35322j1 | \([1, 1, 0, -111870, 20539764]\) | \(-260305116625/157151232\) | \(-93477217717481472\) | \([2]\) | \(403200\) | \(1.9585\) | \(\Gamma_0(N)\)-optimal |
| 35322.f4 | 35322j3 | \([1, 1, 0, 897330, -287024028]\) | \(134335727363375/137728390128\) | \(-81924058411920575088\) | \([2]\) | \(1209600\) | \(2.5079\) |
Rank
sage: E.rank()
The elliptic curves in class 35322.f have rank \(0\).
Complex multiplication
The elliptic curves in class 35322.f do not have complex multiplication.Modular form 35322.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
