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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 37440ft
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.ey2 | 37440ft1 | \([0, 0, 0, -30252, -2131504]\) | \(-16022066761/998400\) | \(-190797211238400\) | \([2]\) | \(122880\) | \(1.4943\) | \(\Gamma_0(N)\)-optimal |
| 37440.ey1 | 37440ft2 | \([0, 0, 0, -491052, -132445744]\) | \(68523370149961/243360\) | \(46506820239360\) | \([2]\) | \(245760\) | \(1.8409\) |
Rank
sage: E.rank()
The elliptic curves in class 37440ft have rank \(1\).
Complex multiplication
The elliptic curves in class 37440ft do not have complex multiplication.Modular form 37440.2.a.ft
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.
