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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 15456t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15456.p3 | 15456t1 | \([0, 1, 0, -134, -264]\) | \(4188852928/2099601\) | \(134374464\) | \([2, 2]\) | \(4096\) | \(0.25244\) | \(\Gamma_0(N)\)-optimal |
| 15456.p1 | 15456t2 | \([0, 1, 0, -1744, -28600]\) | \(1146415874696/1056321\) | \(540836352\) | \([2]\) | \(8192\) | \(0.59901\) | |
| 15456.p2 | 15456t3 | \([0, 1, 0, -1169, 14847]\) | \(43169672512/497007\) | \(2035740672\) | \([4]\) | \(8192\) | \(0.59901\) | |
| 15456.p4 | 15456t4 | \([0, 1, 0, 496, -1524]\) | \(26304066424/17629983\) | \(-9026551296\) | \([2]\) | \(8192\) | \(0.59901\) |
Rank
sage: E.rank()
The elliptic curves in class 15456t have rank \(0\).
Complex multiplication
The elliptic curves in class 15456t do not have complex multiplication.Modular form 15456.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
