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SageMath
E = EllipticCurve("fs1")
E.isogeny_class()
Elliptic curves in class 388080.fs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.fs1 | 388080fs2 | \([0, 0, 0, -77763, 1085938]\) | \(592143556/336875\) | \(29585881100160000\) | \([2]\) | \(2359296\) | \(1.8504\) | |
| 388080.fs2 | 388080fs1 | \([0, 0, 0, 19257, 135142]\) | \(35969456/21175\) | \(-464920988716800\) | \([2]\) | \(1179648\) | \(1.5038\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388080.fs have rank \(0\).
Complex multiplication
The elliptic curves in class 388080.fs do not have complex multiplication.Modular form 388080.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
