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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 426888.ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
426888.ca1 | 426888ca1 | \([0, 0, 0, -28334691, 58007996046]\) | \(598885164/539\) | \(2264249942251799749632\) | \([2]\) | \(30965760\) | \(3.0220\) | \(\Gamma_0(N)\)-optimal |
426888.ca2 | 426888ca2 | \([0, 0, 0, -21931371, 84928833990]\) | \(-138853062/290521\) | \(-2440861437747440130103296\) | \([2]\) | \(61931520\) | \(3.3686\) |
Rank
sage: E.rank()
The elliptic curves in class 426888.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 426888.ca do not have complex multiplication.Modular form 426888.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.