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SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 22050.fb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22050.fb1 | 22050de1 | \([1, -1, 1, -2330, -42703]\) | \(-67645179/8\) | \(-165375000\) | \([]\) | \(15552\) | \(0.60250\) | \(\Gamma_0(N)\)-optimal |
22050.fb2 | 22050de2 | \([1, -1, 1, 295, -133703]\) | \(189/512\) | \(-7715736000000\) | \([]\) | \(46656\) | \(1.1518\) |
Rank
sage: E.rank()
The elliptic curves in class 22050.fb have rank \(1\).
Complex multiplication
The elliptic curves in class 22050.fb do not have complex multiplication.Modular form 22050.2.a.fb
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.