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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 19800n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19800.e4 | 19800n1 | \([0, 0, 0, 150, -19375]\) | \(2048/891\) | \(-162384750000\) | \([2]\) | \(24576\) | \(0.83020\) | \(\Gamma_0(N)\)-optimal |
| 19800.e3 | 19800n2 | \([0, 0, 0, -9975, -373750]\) | \(37642192/1089\) | \(3175524000000\) | \([2, 2]\) | \(49152\) | \(1.1768\) | |
| 19800.e1 | 19800n3 | \([0, 0, 0, -158475, -24282250]\) | \(37736227588/33\) | \(384912000000\) | \([2]\) | \(98304\) | \(1.5233\) | |
| 19800.e2 | 19800n4 | \([0, 0, 0, -23475, 854750]\) | \(122657188/43923\) | \(512317872000000\) | \([2]\) | \(98304\) | \(1.5233\) |
Rank
sage: E.rank()
The elliptic curves in class 19800n have rank \(1\).
Complex multiplication
The elliptic curves in class 19800n do not have complex multiplication.Modular form 19800.2.a.n
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.
