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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 4851n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4851.k1 | 4851n1 | \([0, 0, 1, -39396, 3009739]\) | \(-78843215872/539\) | \(-46227939219\) | \([]\) | \(9600\) | \(1.2273\) | \(\Gamma_0(N)\)-optimal |
| 4851.k2 | 4851n2 | \([0, 0, 1, -21756, 5710864]\) | \(-13278380032/156590819\) | \(-13430187129843099\) | \([]\) | \(28800\) | \(1.7766\) | |
| 4851.k3 | 4851n3 | \([0, 0, 1, 194334, -147821081]\) | \(9463555063808/115539436859\) | \(-9909369321920853939\) | \([]\) | \(86400\) | \(2.3259\) |
Rank
sage: E.rank()
The elliptic curves in class 4851n have rank \(0\).
Complex multiplication
The elliptic curves in class 4851n do not have complex multiplication.Modular form 4851.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
