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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 83490v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83490.u2 | 83490v1 | \([1, 0, 1, 16211, 820136]\) | \(265971760991/317400000\) | \(-562293461400000\) | \([2]\) | \(336000\) | \(1.5165\) | \(\Gamma_0(N)\)-optimal |
83490.u1 | 83490v2 | \([1, 0, 1, -95109, 7811032]\) | \(53706380371489/16171875000\) | \(28649463046875000\) | \([2]\) | \(672000\) | \(1.8631\) |
Rank
sage: E.rank()
The elliptic curves in class 83490v have rank \(0\).
Complex multiplication
The elliptic curves in class 83490v do not have complex multiplication.Modular form 83490.2.a.v
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 Cremona 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 Cremona labels.