Show commands:
SageMath
E = EllipticCurve("fs1")
E.isogeny_class()
Elliptic curves in class 346560.fs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346560.fs1 | 346560fs3 | \([0, 1, 0, -11378258401, 467152068536735]\) | \(13209596798923694545921/92340\) | \(1138810329901301760\) | \([2]\) | \(265420800\) | \(3.9994\) | |
| 346560.fs2 | 346560fs4 | \([0, 1, 0, -719921121, 7109585714079]\) | \(3345930611358906241/165622259047500\) | \(2042585439299137266647040000\) | \([2]\) | \(265420800\) | \(3.9994\) | |
| 346560.fs3 | 346560fs2 | \([0, 1, 0, -711141601, 7299063558815]\) | \(3225005357698077121/8526675600\) | \(105157745863086204518400\) | \([2, 2]\) | \(132710400\) | \(3.6529\) | |
| 346560.fs4 | 346560fs1 | \([0, 1, 0, -43898081, 116987758239]\) | \(-758575480593601/40535043840\) | \(-499910403378753841397760\) | \([2]\) | \(66355200\) | \(3.3063\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.fs have rank \(2\).
Complex multiplication
The elliptic curves in class 346560.fs do not have complex multiplication.Modular form 346560.2.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.
