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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 25242.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25242.f1 | 25242f2 | \([1, 0, 0, -3803351, -3695953923]\) | \(-6084472608417988103640049/2379033678299675392884\) | \(-2379033678299675392884\) | \([]\) | \(1531152\) | \(2.8109\) | |
25242.f2 | 25242f1 | \([1, 0, 0, -89291, 12097137]\) | \(-78731237277328508209/17734929828102144\) | \(-17734929828102144\) | \([7]\) | \(218736\) | \(1.8380\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25242.f have rank \(0\).
Complex multiplication
The elliptic curves in class 25242.f do not have complex multiplication.Modular form 25242.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.