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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 232730h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
232730.h2 | 232730h1 | \([1, 0, 1, 546202, -48188744]\) | \(7023836099951/4456448000\) | \(-11434026323935232000\) | \([]\) | \(4173120\) | \(2.3459\) | \(\Gamma_0(N)\)-optimal |
232730.h1 | 232730h2 | \([1, 0, 1, -9091558, -10892245832]\) | \(-32391289681150609/1228250000000\) | \(-3151353461854250000000\) | \([]\) | \(12519360\) | \(2.8952\) |
Rank
sage: E.rank()
The elliptic curves in class 232730h have rank \(1\).
Complex multiplication
The elliptic curves in class 232730h do not have complex multiplication.Modular form 232730.2.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 Cremona 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 Cremona labels.