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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 211582.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
211582.r1 | 211582b2 | \([1, -1, 1, -172538463, 872366394183]\) | \(-11592721552621292758609928721/13988979997751115776\) | \(-685460019889804673024\) | \([7]\) | \(71124480\) | \(3.2793\) | |
211582.r2 | 211582b1 | \([1, -1, 1, 469827, -32919435]\) | \(234068198293557237519/144942233965016816\) | \(-7102169464285823984\) | \([]\) | \(10160640\) | \(2.3064\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 211582.r have rank \(1\).
Complex multiplication
The elliptic curves in class 211582.r do not have complex multiplication.Modular form 211582.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.