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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 9450.ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.ca1 | 9450ck1 | \([1, -1, 1, -110, 487]\) | \(-296595/14\) | \(-6889050\) | \([]\) | \(3240\) | \(0.074970\) | \(\Gamma_0(N)\)-optimal |
9450.ca2 | 9450ck2 | \([1, -1, 1, 565, 1027]\) | \(4511445/2744\) | \(-12152284200\) | \([]\) | \(9720\) | \(0.62428\) |
Rank
sage: E.rank()
The elliptic curves in class 9450.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 9450.ca do not have complex multiplication.Modular form 9450.2.a.ca
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.