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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 222376.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
222376.h1 | 222376f2 | \([0, 1, 0, -8228032, -6374359920]\) | \(1278763167594532/375974556419\) | \(18112567542083645582336\) | \([2]\) | \(13271040\) | \(2.9767\) | |
222376.h2 | 222376f1 | \([0, 1, 0, 1381788, -662282912]\) | \(24226243449392/29774625727\) | \(-358598015685627004672\) | \([2]\) | \(6635520\) | \(2.6302\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 222376.h have rank \(0\).
Complex multiplication
The elliptic curves in class 222376.h do not have complex multiplication.Modular form 222376.2.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.