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SageMath
E = EllipticCurve("fi1")
E.isogeny_class()
Elliptic curves in class 25200fi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25200.b1 | 25200fi1 | \([0, 0, 0, -64875, 6156250]\) | \(5177717/189\) | \(1102248000000000\) | \([2]\) | \(122880\) | \(1.6560\) | \(\Gamma_0(N)\)-optimal |
25200.b2 | 25200fi2 | \([0, 0, 0, 25125, 21906250]\) | \(300763/35721\) | \(-208324872000000000\) | \([2]\) | \(245760\) | \(2.0025\) |
Rank
sage: E.rank()
The elliptic curves in class 25200fi have rank \(0\).
Complex multiplication
The elliptic curves in class 25200fi do not have complex multiplication.Modular form 25200.2.a.fi
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.