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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 46818.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46818.j1 | 46818k2 | \([1, -1, 1, -16094, -854063]\) | \(-35937/4\) | \(-51310775227716\) | \([]\) | \(181440\) | \(1.3681\) | |
46818.j2 | 46818k1 | \([1, -1, 1, 1246, 1377]\) | \(109503/64\) | \(-125129157696\) | \([]\) | \(60480\) | \(0.81880\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46818.j have rank \(0\).
Complex multiplication
The elliptic curves in class 46818.j do not have complex multiplication.Modular form 46818.2.a.j
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.