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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 151620.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
151620.h1 | 151620k1 | \([0, -1, 0, -1925, -11298]\) | \(1048576/525\) | \(395185400400\) | \([2]\) | \(171072\) | \(0.91801\) | \(\Gamma_0(N)\)-optimal |
151620.h2 | 151620k2 | \([0, -1, 0, 7100, -94328]\) | \(3286064/2205\) | \(-26556458906880\) | \([2]\) | \(342144\) | \(1.2646\) |
Rank
sage: E.rank()
The elliptic curves in class 151620.h have rank \(0\).
Complex multiplication
The elliptic curves in class 151620.h do not have complex multiplication.Modular form 151620.2.a.h
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.