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SageMath
E = EllipticCurve("ft1")
E.isogeny_class()
Elliptic curves in class 304200.ft
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304200.ft1 | 304200ft3 | \([0, 0, 0, -11572275, 14780866750]\) | \(3044193988/85293\) | \(4801987385711568000000\) | \([2]\) | \(22020096\) | \(2.9393\) | |
| 304200.ft2 | 304200ft2 | \([0, 0, 0, -1685775, -513548750]\) | \(37642192/13689\) | \(192672333377316000000\) | \([2, 2]\) | \(11010048\) | \(2.5928\) | |
| 304200.ft3 | 304200ft1 | \([0, 0, 0, -1495650, -703863875]\) | \(420616192/117\) | \(102923255009250000\) | \([2]\) | \(5505024\) | \(2.2462\) | \(\Gamma_0(N)\)-optimal |
| 304200.ft4 | 304200ft4 | \([0, 0, 0, 5158725, -3627796250]\) | \(269676572/257049\) | \(-14471833040340624000000\) | \([2]\) | \(22020096\) | \(2.9393\) |
Rank
sage: E.rank()
The elliptic curves in class 304200.ft have rank \(1\).
Complex multiplication
The elliptic curves in class 304200.ft do not have complex multiplication.Modular form 304200.2.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 LMFDB 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 LMFDB labels.
