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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 25350.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25350.n1 | 25350o2 | \([1, 1, 0, -276825, 50335875]\) | \(248858189/27378\) | \(258102298441406250\) | \([2]\) | \(430080\) | \(2.0744\) | |
| 25350.n2 | 25350o1 | \([1, 1, 0, -65575, -5645375]\) | \(3307949/468\) | \(4412005101562500\) | \([2]\) | \(215040\) | \(1.7279\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25350.n have rank \(0\).
Complex multiplication
The elliptic curves in class 25350.n do not have complex multiplication.Modular form 25350.2.a.n
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.
