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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 4290.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4290.f1 | 4290g2 | \([1, 1, 0, -775522, 262503874]\) | \(51583042491609575206441/9586057511268810\) | \(9586057511268810\) | \([2]\) | \(64512\) | \(2.0688\) | |
4290.f2 | 4290g1 | \([1, 1, 0, -43472, 4968684]\) | \(-9085904860560159241/5484993611139900\) | \(-5484993611139900\) | \([2]\) | \(32256\) | \(1.7222\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4290.f have rank \(0\).
Complex multiplication
The elliptic curves in class 4290.f do not have complex multiplication.Modular form 4290.2.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.