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SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 243360.ff
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 243360.ff1 | 243360ff4 | \([0, 0, 0, -346058427, -2477068906754]\) | \(2543984126301795848/909361981125\) | \(1638303640357987077696000\) | \([2]\) | \(66060288\) | \(3.6156\) | |
| 243360.ff2 | 243360ff2 | \([0, 0, 0, -178748427, 900920753746]\) | \(350584567631475848/8259273550125\) | \(14879880844746068234304000\) | \([2]\) | \(66060288\) | \(3.6156\) | |
| 243360.ff3 | 243360ff1 | \([0, 0, 0, -24747177, -26813576504]\) | \(7442744143086784/2927948765625\) | \(659372892900519681000000\) | \([2, 2]\) | \(33030144\) | \(3.2690\) | \(\Gamma_0(N)\)-optimal |
| 243360.ff4 | 243360ff3 | \([0, 0, 0, 79357668, -193547896256]\) | \(3834800837445824/3342041015625\) | \(-48168083344329000000000000\) | \([2]\) | \(66060288\) | \(3.6156\) |
Rank
sage: E.rank()
The elliptic curves in class 243360.ff have rank \(0\).
Complex multiplication
The elliptic curves in class 243360.ff do not have complex multiplication.Modular form 243360.2.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 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.
