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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 18480ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.cj3 | 18480ct1 | \([0, 1, 0, -8016, 237204]\) | \(13908844989649/1980372240\) | \(8111604695040\) | \([2]\) | \(36864\) | \(1.2028\) | \(\Gamma_0(N)\)-optimal |
| 18480.cj2 | 18480ct2 | \([0, 1, 0, -33936, -2178540]\) | \(1055257664218129/115307784900\) | \(472300686950400\) | \([2, 2]\) | \(73728\) | \(1.5494\) | |
| 18480.cj1 | 18480ct3 | \([0, 1, 0, -527856, -147786156]\) | \(3971101377248209009/56495958750\) | \(231407447040000\) | \([2]\) | \(147456\) | \(1.8959\) | |
| 18480.cj4 | 18480ct4 | \([0, 1, 0, 45264, -10763820]\) | \(2503876820718671/13702874328990\) | \(-56126973251543040\) | \([2]\) | \(147456\) | \(1.8959\) |
Rank
sage: E.rank()
The elliptic curves in class 18480ct have rank \(1\).
Complex multiplication
The elliptic curves in class 18480ct do not have complex multiplication.Modular form 18480.2.a.ct
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
