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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 51842.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51842.f1 | 51842b2 | \([1, -1, 0, -22892, 1326884]\) | \(926859375/9604\) | \(13747505418332\) | \([2]\) | \(110592\) | \(1.3380\) | |
51842.f2 | 51842b1 | \([1, -1, 0, -352, 51120]\) | \(-3375/784\) | \(-1122245340272\) | \([2]\) | \(55296\) | \(0.99145\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 51842.f have rank \(1\).
Complex multiplication
The elliptic curves in class 51842.f do not have complex multiplication.Modular form 51842.2.a.f
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.