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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 18032s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18032.x2 | 18032s1 | \([0, -1, 0, -3432, -76432]\) | \(-3183010111/8464\) | \(-11891310592\) | \([2]\) | \(12288\) | \(0.80801\) | \(\Gamma_0(N)\)-optimal |
| 18032.x1 | 18032s2 | \([0, -1, 0, -54952, -4939920]\) | \(13062552753151/92\) | \(129253376\) | \([2]\) | \(24576\) | \(1.1546\) |
Rank
sage: E.rank()
The elliptic curves in class 18032s have rank \(1\).
Complex multiplication
The elliptic curves in class 18032s do not have complex multiplication.Modular form 18032.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
