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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 18513n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18513.j2 | 18513n1 | \([0, 0, 1, 726, -36270]\) | \(32768/459\) | \(-592783797771\) | \([]\) | \(21600\) | \(0.93972\) | \(\Gamma_0(N)\)-optimal |
| 18513.j1 | 18513n2 | \([0, 0, 1, -64614, -6325245]\) | \(-23100424192/14739\) | \(-19034946395091\) | \([]\) | \(64800\) | \(1.4890\) |
Rank
sage: E.rank()
The elliptic curves in class 18513n have rank \(1\).
Complex multiplication
The elliptic curves in class 18513n do not have complex multiplication.Modular form 18513.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
