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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 62400ej
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62400.dz4 | 62400ej1 | \([0, -1, 0, -461633, -199288863]\) | \(-2656166199049/2658140160\) | \(-10887742095360000000\) | \([2]\) | \(1474560\) | \(2.3486\) | \(\Gamma_0(N)\)-optimal |
| 62400.dz3 | 62400ej2 | \([0, -1, 0, -8653633, -9792120863]\) | \(17496824387403529/6580454400\) | \(26953541222400000000\) | \([2, 2]\) | \(2949120\) | \(2.6951\) | |
| 62400.dz2 | 62400ej3 | \([0, -1, 0, -9933633, -6703480863]\) | \(26465989780414729/10571870144160\) | \(43302380110479360000000\) | \([2]\) | \(5898240\) | \(3.0417\) | |
| 62400.dz1 | 62400ej4 | \([0, -1, 0, -138445633, -626953080863]\) | \(71647584155243142409/10140000\) | \(41533440000000000\) | \([2]\) | \(5898240\) | \(3.0417\) |
Rank
sage: E.rank()
The elliptic curves in class 62400ej have rank \(0\).
Complex multiplication
The elliptic curves in class 62400ej do not have complex multiplication.Modular form 62400.2.a.ej
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.
