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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 83790h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83790.q2 | 83790h1 | \([1, -1, 0, -2445, -50779]\) | \(-239483061/30400\) | \(-205238577600\) | \([2]\) | \(101376\) | \(0.90450\) | \(\Gamma_0(N)\)-optimal |
83790.q1 | 83790h2 | \([1, -1, 0, -40245, -3097459]\) | \(1067776023861/14440\) | \(97488324360\) | \([2]\) | \(202752\) | \(1.2511\) |
Rank
sage: E.rank()
The elliptic curves in class 83790h have rank \(1\).
Complex multiplication
The elliptic curves in class 83790h do not have complex multiplication.Modular form 83790.2.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.