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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 414736h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414736.h2 | 414736h1 | \([0, 1, 0, 108652192, -64310520380]\) | \(7953970437500/4703287687\) | \(-83879678455744055618771968\) | \([2]\) | \(97320960\) | \(3.6636\) | \(\Gamma_0(N)\)-optimal* |
414736.h1 | 414736h2 | \([0, 1, 0, -439836168, -517800696428]\) | \(263822189935250/149429406721\) | \(5329927243121702619223820288\) | \([2]\) | \(194641920\) | \(4.0102\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414736h have rank \(1\).
Complex multiplication
The elliptic curves in class 414736h do not have complex multiplication.Modular form 414736.2.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.