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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 3024.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3024.p1 | 3024m3 | \([0, 0, 0, -152955, 23024682]\) | \(-545407363875/14\) | \(-10158317568\) | \([]\) | \(7776\) | \(1.4363\) | |
| 3024.p2 | 3024m2 | \([0, 0, 0, -1755, 36234]\) | \(-7414875/2744\) | \(-221225582592\) | \([]\) | \(2592\) | \(0.88703\) | |
| 3024.p3 | 3024m1 | \([0, 0, 0, 165, -502]\) | \(4492125/3584\) | \(-396361728\) | \([]\) | \(864\) | \(0.33772\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3024.p have rank \(0\).
Complex multiplication
The elliptic curves in class 3024.p do not have complex multiplication.Modular form 3024.2.a.p
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.
