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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 16762.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16762.h1 | 16762i2 | \([1, 0, 0, -131501, -18489883]\) | \(-10418796526321/82044596\) | \(-1980357097027124\) | \([]\) | \(83200\) | \(1.7638\) | |
16762.h2 | 16762i1 | \([1, 0, 0, 1439, 35017]\) | \(13651919/29696\) | \(-716789249024\) | \([]\) | \(16640\) | \(0.95905\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16762.h have rank \(1\).
Complex multiplication
The elliptic curves in class 16762.h do not have complex multiplication.Modular form 16762.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.