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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 101430h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.b2 | 101430h1 | \([1, -1, 0, -3078630, 2638321076]\) | \(-1015884369980369163/358196480000000\) | \(-1137819357239040000000\) | \([2]\) | \(6773760\) | \(2.7513\) | \(\Gamma_0(N)\)-optimal |
101430.b1 | 101430h2 | \([1, -1, 0, -52846950, 147872232500]\) | \(5138442430700033888523/413281250000000\) | \(1312797396093750000000\) | \([2]\) | \(13547520\) | \(3.0979\) |
Rank
sage: E.rank()
The elliptic curves in class 101430h have rank \(1\).
Complex multiplication
The elliptic curves in class 101430h do not have complex multiplication.Modular form 101430.2.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.