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SageMath
E = EllipticCurve("gr1")
E.isogeny_class()
Elliptic curves in class 169050.gr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169050.gr1 | 169050et2 | \([1, 1, 1, -24403, -1510279]\) | \(-11151419545/292008\) | \(-42084200260200\) | \([]\) | \(653184\) | \(1.3970\) | |
169050.gr2 | 169050et1 | \([1, 1, 1, 1322, -7939]\) | \(1772855/1242\) | \(-178997071050\) | \([]\) | \(217728\) | \(0.84773\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 169050.gr have rank \(1\).
Complex multiplication
The elliptic curves in class 169050.gr do not have complex multiplication.Modular form 169050.2.a.gr
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.