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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 9450.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9450.cl1 | 9450dd3 | \([1, -1, 1, -26555, 1672197]\) | \(-545407363875/14\) | \(-53156250\) | \([]\) | \(15552\) | \(0.99860\) | |
| 9450.cl2 | 9450dd1 | \([1, -1, 1, -305, 2697]\) | \(-7414875/2744\) | \(-1157625000\) | \([]\) | \(5184\) | \(0.44930\) | \(\Gamma_0(N)\)-optimal |
| 9450.cl3 | 9450dd2 | \([1, -1, 1, 2320, -27053]\) | \(4492125/3584\) | \(-1102248000000\) | \([]\) | \(15552\) | \(0.99860\) |
Rank
sage: E.rank()
The elliptic curves in class 9450.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 9450.cl do not have complex multiplication.Modular form 9450.2.a.cl
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.
