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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 25200en
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25200.fh2 | 25200en1 | \([0, 0, 0, 645, 5290]\) | \(397535/392\) | \(-29262643200\) | \([]\) | \(17280\) | \(0.69528\) | \(\Gamma_0(N)\)-optimal |
25200.fh1 | 25200en2 | \([0, 0, 0, -6555, -287030]\) | \(-417267265/235298\) | \(-17564901580800\) | \([]\) | \(51840\) | \(1.2446\) |
Rank
sage: E.rank()
The elliptic curves in class 25200en have rank \(0\).
Complex multiplication
The elliptic curves in class 25200en do not have complex multiplication.Modular form 25200.2.a.en
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 Cremona 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 Cremona labels.