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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 32368.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32368.q1 | 32368a4 | \([0, 0, 0, -86411, -9776870]\) | \(1443468546/7\) | \(346036189184\) | \([2]\) | \(73728\) | \(1.4146\) | |
| 32368.q2 | 32368a3 | \([0, 0, 0, -17051, 677994]\) | \(11090466/2401\) | \(118690412890112\) | \([2]\) | \(73728\) | \(1.4146\) | |
| 32368.q3 | 32368a2 | \([0, 0, 0, -5491, -147390]\) | \(740772/49\) | \(1211126662144\) | \([2, 2]\) | \(36864\) | \(1.0680\) | |
| 32368.q4 | 32368a1 | \([0, 0, 0, 289, -9826]\) | \(432/7\) | \(-43254523648\) | \([2]\) | \(18432\) | \(0.72143\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32368.q have rank \(1\).
Complex multiplication
The elliptic curves in class 32368.q do not have complex multiplication.Modular form 32368.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
