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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 15210.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15210.w1 | 15210e4 | \([1, -1, 0, -6082764, -5772781702]\) | \(261984288445803/42250\) | \(4014006945360750\) | \([2]\) | \(580608\) | \(2.3963\) | |
| 15210.w2 | 15210e3 | \([1, -1, 0, -379014, -90705952]\) | \(-63378025803/812500\) | \(-77192441256937500\) | \([2]\) | \(290304\) | \(2.0497\) | |
| 15210.w3 | 15210e2 | \([1, -1, 0, -84954, -5687460]\) | \(520300455507/193072360\) | \(25161931932279480\) | \([2]\) | \(193536\) | \(1.8470\) | |
| 15210.w4 | 15210e1 | \([1, -1, 0, 16446, -637740]\) | \(3774555693/3515200\) | \(-458114372913600\) | \([2]\) | \(96768\) | \(1.5004\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15210.w have rank \(0\).
Complex multiplication
The elliptic curves in class 15210.w do not have complex multiplication.Modular form 15210.2.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 LMFDB 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 LMFDB labels.
