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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 388416.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388416.z1 | 388416z2 | \([0, -1, 0, -583009, -167243615]\) | \(5639752/147\) | \(571225467946893312\) | \([2]\) | \(5013504\) | \(2.1889\) | |
| 388416.z2 | 388416z1 | \([0, -1, 0, 6551, -8416151]\) | \(64/63\) | \(-30601364354297856\) | \([2]\) | \(2506752\) | \(1.8423\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388416.z have rank \(1\).
Complex multiplication
The elliptic curves in class 388416.z do not have complex multiplication.Modular form 388416.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
