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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 362805h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
362805.h2 | 362805h1 | \([0, -1, 1, 86159, -1507914]\) | \(1503484706816/890163675\) | \(-41878534324572675\) | \([]\) | \(3447360\) | \(1.8788\) | \(\Gamma_0(N)\)-optimal |
362805.h1 | 362805h2 | \([0, -1, 1, -1083481, 479828187]\) | \(-2989967081734144/380653171875\) | \(-17908163826303796875\) | \([]\) | \(10342080\) | \(2.4281\) |
Rank
sage: E.rank()
The elliptic curves in class 362805h have rank \(0\).
Complex multiplication
The elliptic curves in class 362805h do not have complex multiplication.Modular form 362805.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.