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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 193200el
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193200.k1 | 193200el1 | \([0, -1, 0, -47755008, -126999871488]\) | \(188191720927962271801/9422571110400\) | \(603044551065600000000\) | \([2]\) | \(15925248\) | \(3.0583\) | \(\Gamma_0(N)\)-optimal |
| 193200.k2 | 193200el2 | \([0, -1, 0, -45195008, -141223231488]\) | \(-159520003524722950201/42335913815758080\) | \(-2709498484208517120000000\) | \([2]\) | \(31850496\) | \(3.4049\) |
Rank
sage: E.rank()
The elliptic curves in class 193200el have rank \(0\).
Complex multiplication
The elliptic curves in class 193200el do not have complex multiplication.Modular form 193200.2.a.el
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
