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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 372232.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
372232.h1 | 372232h2 | \([0, 0, 0, -282931, 57924270]\) | \(50668941906/1127\) | \(55711826458624\) | \([2]\) | \(1261568\) | \(1.7525\) | |
372232.h2 | 372232h1 | \([0, 0, 0, -17051, 972774]\) | \(-22180932/3703\) | \(-91526572039168\) | \([2]\) | \(630784\) | \(1.4060\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 372232.h have rank \(1\).
Complex multiplication
The elliptic curves in class 372232.h do not have complex multiplication.Modular form 372232.2.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.