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SageMath
E = EllipticCurve("hs1")
E.isogeny_class()
Elliptic curves in class 103488hs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
103488.ia2 | 103488hs1 | \([0, 1, 0, -15157, 829835]\) | \(-3196715008/649539\) | \(-78251636542464\) | \([2]\) | \(345600\) | \(1.3883\) | \(\Gamma_0(N)\)-optimal |
103488.ia1 | 103488hs2 | \([0, 1, 0, -253297, 48981743]\) | \(932410994128/29403\) | \(56676082434048\) | \([2]\) | \(691200\) | \(1.7349\) |
Rank
sage: E.rank()
The elliptic curves in class 103488hs have rank \(0\).
Complex multiplication
The elliptic curves in class 103488hs do not have complex multiplication.Modular form 103488.2.a.hs
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.