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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 59584.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59584.u1 | 59584bn3 | \([0, 1, 0, -150789, 22487149]\) | \(-50357871050752/19\) | \(-143061184\) | \([]\) | \(163296\) | \(1.3530\) | |
| 59584.u2 | 59584bn2 | \([0, 1, 0, -1829, 31429]\) | \(-89915392/6859\) | \(-51645087424\) | \([]\) | \(54432\) | \(0.80366\) | |
| 59584.u3 | 59584bn1 | \([0, 1, 0, 131, 69]\) | \(32768/19\) | \(-143061184\) | \([]\) | \(18144\) | \(0.25436\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 59584.u have rank \(1\).
Complex multiplication
The elliptic curves in class 59584.u do not have complex multiplication.Modular form 59584.2.a.u
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 LMFDB 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 LMFDB labels.
