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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 24882h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24882.k2 | 24882h1 | \([1, 1, 0, -158898, -640800]\) | \(443693713490687867689/256624567753198788\) | \(256624567753198788\) | \([2]\) | \(629760\) | \(2.0300\) | \(\Gamma_0(N)\)-optimal |
24882.k1 | 24882h2 | \([1, 1, 0, -1769408, -904136910]\) | \(612643817473977455499529/1970680400816616918\) | \(1970680400816616918\) | \([2]\) | \(1259520\) | \(2.3766\) |
Rank
sage: E.rank()
The elliptic curves in class 24882h have rank \(1\).
Complex multiplication
The elliptic curves in class 24882h do not have complex multiplication.Modular form 24882.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.