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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 14490.ca
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.ca1 | 14490bi1 | \([1, -1, 1, -4926602, -1758530871]\) | \(489781415227546051766883/233890092903563264000\) | \(6315032508396208128000\) | \([2]\) | \(1032192\) | \(2.8770\) | \(\Gamma_0(N)\)-optimal |
14490.ca2 | 14490bi2 | \([1, -1, 1, 17683318, -13389073719]\) | \(22649115256119592694355357/15973509811739648000000\) | \(-431284764916970496000000\) | \([2]\) | \(2064384\) | \(3.2236\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.ca have rank \(1\).
Complex multiplication
The elliptic curves in class 14490.ca do not have complex multiplication.Modular form 14490.2.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.