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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 490049.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
490049.b1 | 490049b2 | \([1, -1, 0, -214727, -17850736]\) | \(9306718526813625/4208725560473\) | \(495152353464087977\) | \([2]\) | \(3784704\) | \(2.0905\) | \(\Gamma_0(N)\)-optimal* |
490049.b2 | 490049b1 | \([1, -1, 0, -181162, -29618625]\) | \(5589051871019625/3289698937\) | \(387029790239113\) | \([2]\) | \(1892352\) | \(1.7439\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 490049.b have rank \(1\).
Complex multiplication
The elliptic curves in class 490049.b do not have complex multiplication.Modular form 490049.2.a.b
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.