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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 5390.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5390.l1 | 5390r2 | \([1, -1, 0, -7077569, 4149275325]\) | \(971613907622044623/378125000000000\) | \(15258707646875000000000\) | \([2]\) | \(451584\) | \(2.9554\) | |
5390.l2 | 5390r1 | \([1, -1, 0, -6199489, 5941085373]\) | \(652993822364173263/225280000000\) | \(9090860584960000000\) | \([2]\) | \(225792\) | \(2.6088\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5390.l have rank \(0\).
Complex multiplication
The elliptic curves in class 5390.l do not have complex multiplication.Modular form 5390.2.a.l
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.