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Properties

Label 259182.ff
Number of curves $2$
Conductor $259182$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ff1")
 
E.isogeny_class()
 

Elliptic curves in class 259182.ff

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.ff1 259182ff2 \([1, -1, 1, -150277304, 709106072491]\) \(8086832279405361/226576\) \(10515728489856902928\) \([2]\) \(32440320\) \(3.1607\)  
259182.ff2 259182ff1 \([1, -1, 1, -9404264, 11051984683]\) \(1981858514481/10449152\) \(484960655061635993856\) \([2]\) \(16220160\) \(2.8141\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 259182.ff have rank \(0\).

Complex multiplication

The elliptic curves in class 259182.ff do not have complex multiplication.

Modular form 259182.2.a.ff

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2 q^{5} - q^{7} + q^{8} + 2 q^{10} - 4 q^{13} - q^{14} + q^{16} - q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.