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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4761.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4761.b1 | 4761c2 | \([1, -1, 1, -73895, -7687420]\) | \(413493625/1587\) | \(171266124809547\) | \([2]\) | \(16896\) | \(1.5897\) | |
4761.b2 | 4761c1 | \([1, -1, 1, -2480, -231694]\) | \(-15625/207\) | \(-22339059757767\) | \([2]\) | \(8448\) | \(1.2431\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4761.b have rank \(1\).
Complex multiplication
The elliptic curves in class 4761.b do not have complex multiplication.Modular form 4761.2.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.