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SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 273600ff
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 273600.ff3 | 273600ff1 | \([0, 0, 0, -372542700, -2793064754000]\) | \(-1914980734749238129/20440940544000\) | \(-61036321409335296000000000\) | \([2]\) | \(106168320\) | \(3.7642\) | \(\Gamma_0(N)\)-optimal |
| 273600.ff2 | 273600ff2 | \([0, 0, 0, -5975870700, -177807411506000]\) | \(7903870428425797297009/886464000000\) | \(2646967320576000000000000\) | \([2]\) | \(212336640\) | \(4.1108\) | |
| 273600.ff4 | 273600ff3 | \([0, 0, 0, 1231041300, -14539151666000]\) | \(69096190760262356111/70568821500000000\) | \(-210717371897856000000000000000\) | \([2]\) | \(318504960\) | \(4.3135\) | |
| 273600.ff1 | 273600ff4 | \([0, 0, 0, -6670526700, -133900237874000]\) | \(10993009831928446009969/3767761230468750000\) | \(11250474750000000000000000000000\) | \([2]\) | \(637009920\) | \(4.6601\) |
Rank
sage: E.rank()
The elliptic curves in class 273600ff have rank \(0\).
Complex multiplication
The elliptic curves in class 273600ff do not have complex multiplication.Modular form 273600.2.a.ff
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
