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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 37440.dx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.dx1 | 37440ct2 | \([0, 0, 0, -491052, 132445744]\) | \(68523370149961/243360\) | \(46506820239360\) | \([2]\) | \(245760\) | \(1.8409\) | |
| 37440.dx2 | 37440ct1 | \([0, 0, 0, -30252, 2131504]\) | \(-16022066761/998400\) | \(-190797211238400\) | \([2]\) | \(122880\) | \(1.4943\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37440.dx have rank \(0\).
Complex multiplication
The elliptic curves in class 37440.dx do not have complex multiplication.Modular form 37440.2.a.dx
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.
