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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 3024.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3024.z1 | 3024p2 | \([0, 0, 0, -111, -502]\) | \(-2431344/343\) | \(-21337344\) | \([]\) | \(864\) | \(0.13750\) | |
| 3024.z2 | 3024p1 | \([0, 0, 0, 9, 2]\) | \(11664/7\) | \(-48384\) | \([]\) | \(288\) | \(-0.41181\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3024.z have rank \(0\).
Complex multiplication
The elliptic curves in class 3024.z do not have complex multiplication.Modular form 3024.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
