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SageMath
E = EllipticCurve("fs1")
E.isogeny_class()
Elliptic curves in class 92400.fs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.fs1 | 92400gn4 | \([0, 1, 0, -106445008, -422739196012]\) | \(2084105208962185000201/31185000\) | \(1995840000000000\) | \([2]\) | \(7077888\) | \(2.9394\) | |
| 92400.fs2 | 92400gn3 | \([0, 1, 0, -7213008, -5429436012]\) | \(648474704552553481/176469171805080\) | \(11294026995525120000000\) | \([4]\) | \(7077888\) | \(2.9394\) | |
| 92400.fs3 | 92400gn2 | \([0, 1, 0, -6653008, -6606556012]\) | \(508859562767519881/62240270400\) | \(3983377305600000000\) | \([2, 2]\) | \(3538944\) | \(2.5928\) | |
| 92400.fs4 | 92400gn1 | \([0, 1, 0, -381008, -121308012]\) | \(-95575628340361/43812679680\) | \(-2804011499520000000\) | \([2]\) | \(1769472\) | \(2.2462\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.fs have rank \(0\).
Complex multiplication
The elliptic curves in class 92400.fs do not have complex multiplication.Modular form 92400.2.a.fs
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
