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SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 169050.gh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169050.gh1 | 169050dy2 | \([1, 1, 1, -11242463, -3390304219]\) | \(85486955243540761/46777901234400\) | \(85990207848842587500000\) | \([2]\) | \(14745600\) | \(3.0914\) | |
169050.gh2 | 169050dy1 | \([1, 1, 1, -6734463, 6680567781]\) | \(18374873741826841/136564270080\) | \(251041403291280000000\) | \([2]\) | \(7372800\) | \(2.7449\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 169050.gh have rank \(0\).
Complex multiplication
The elliptic curves in class 169050.gh do not have complex multiplication.Modular form 169050.2.a.gh
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 LMFDB 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 LMFDB labels.