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SageMath
E = EllipticCurve("hu1")
E.isogeny_class()
Elliptic curves in class 169050.hu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169050.hu1 | 169050bg1 | \([1, 0, 0, -28813, -1040383]\) | \(1439069689/579600\) | \(1065458756250000\) | \([2]\) | \(884736\) | \(1.5815\) | \(\Gamma_0(N)\)-optimal |
169050.hu2 | 169050bg2 | \([1, 0, 0, 93687, -7532883]\) | \(49471280711/41992020\) | \(-77192486890312500\) | \([2]\) | \(1769472\) | \(1.9281\) |
Rank
sage: E.rank()
The elliptic curves in class 169050.hu have rank \(1\).
Complex multiplication
The elliptic curves in class 169050.hu do not have complex multiplication.Modular form 169050.2.a.hu
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.