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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 106470.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106470.h1 | 106470bd2 | \([1, -1, 0, -89010, 68172300]\) | \(-22164361129/557375000\) | \(-1961259803787375000\) | \([]\) | \(2177280\) | \(2.1906\) | |
106470.h2 | 106470bd1 | \([1, -1, 0, 9855, -2476629]\) | \(30080231/768950\) | \(-2705738015020950\) | \([]\) | \(725760\) | \(1.6413\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 106470.h have rank \(0\).
Complex multiplication
The elliptic curves in class 106470.h do not have complex multiplication.Modular form 106470.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.