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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 379050.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
379050.f1 | 379050f1 | \([1, 1, 0, -1096725, 747550125]\) | \(-549754417/592704\) | \(-157284777322701000000\) | \([]\) | \(13296960\) | \(2.5703\) | \(\Gamma_0(N)\)-optimal |
379050.f2 | 379050f2 | \([1, 1, 0, 9191775, -13502022375]\) | \(323648023823/484243284\) | \(-128502755328044791312500\) | \([]\) | \(39890880\) | \(3.1196\) |
Rank
sage: E.rank()
The elliptic curves in class 379050.f have rank \(1\).
Complex multiplication
The elliptic curves in class 379050.f do not have complex multiplication.Modular form 379050.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.