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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 14400w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14400.cs4 | 14400w1 | \([0, 0, 0, 825, -24500]\) | \(85184/405\) | \(-295245000000\) | \([2]\) | \(12288\) | \(0.88325\) | \(\Gamma_0(N)\)-optimal |
| 14400.cs3 | 14400w2 | \([0, 0, 0, -9300, -308000]\) | \(1906624/225\) | \(10497600000000\) | \([2, 2]\) | \(24576\) | \(1.2298\) | |
| 14400.cs1 | 14400w3 | \([0, 0, 0, -144300, -21098000]\) | \(890277128/15\) | \(5598720000000\) | \([2]\) | \(49152\) | \(1.5764\) | |
| 14400.cs2 | 14400w4 | \([0, 0, 0, -36300, 2338000]\) | \(14172488/1875\) | \(699840000000000\) | \([2]\) | \(49152\) | \(1.5764\) |
Rank
sage: E.rank()
The elliptic curves in class 14400w have rank \(0\).
Complex multiplication
The elliptic curves in class 14400w do not have complex multiplication.Modular form 14400.2.a.w
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.
