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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 35739h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35739.r1 | 35739h1 | \([1, -1, 0, -1122, -12817]\) | \(1157625/121\) | \(16335689337\) | \([2]\) | \(25920\) | \(0.69471\) | \(\Gamma_0(N)\)-optimal |
35739.r2 | 35739h2 | \([1, -1, 0, 1443, -64630]\) | \(2460375/14641\) | \(-1976618409777\) | \([2]\) | \(51840\) | \(1.0413\) |
Rank
sage: E.rank()
The elliptic curves in class 35739h have rank \(0\).
Complex multiplication
The elliptic curves in class 35739h do not have complex multiplication.Modular form 35739.2.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.