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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 247744.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
247744.h1 | 247744h2 | \([0, 1, 0, -28289, 1559935]\) | \(81182737/12482\) | \(384957105569792\) | \([2]\) | \(884736\) | \(1.5222\) | |
247744.h2 | 247744h1 | \([0, 1, 0, 3071, 136191]\) | \(103823/316\) | \(-9745749508096\) | \([2]\) | \(442368\) | \(1.1756\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 247744.h have rank \(2\).
Complex multiplication
The elliptic curves in class 247744.h do not have complex multiplication.Modular form 247744.2.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.