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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 466578.gb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466578.gb1 | 466578gb2 | \([1, -1, 1, -443666, -113645591]\) | \(-67645179/8\) | \(-1142205838049304\) | \([]\) | \(5132160\) | \(1.9148\) | |
466578.gb2 | 466578gb1 | \([1, -1, 1, 694, -481911]\) | \(189/512\) | \(-100275958347264\) | \([]\) | \(1710720\) | \(1.3655\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 466578.gb have rank \(0\).
Complex multiplication
The elliptic curves in class 466578.gb do not have complex multiplication.Modular form 466578.2.a.gb
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.