Properties

Label 344850fo
Number of curves $2$
Conductor $344850$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fo1")
 
E.isogeny_class()
 

Elliptic curves in class 344850fo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
344850.fo2 344850fo1 \([1, 1, 1, -4404463, 3572343281]\) \(-341370886042369/1817528220\) \(-50310345483615937500\) \([2]\) \(17203200\) \(2.6252\) \(\Gamma_0(N)\)-optimal
344850.fo1 344850fo2 \([1, 1, 1, -70561213, 228108352781]\) \(1403607530712116449/39475350\) \(1092702976896093750\) \([2]\) \(34406400\) \(2.9717\)  

Rank

sage: E.rank()
 

The elliptic curves in class 344850fo have rank \(1\).

Complex multiplication

The elliptic curves in class 344850fo do not have complex multiplication.

Modular form 344850.2.a.fo

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + 2 q^{7} + q^{8} + q^{9} - q^{12} + 6 q^{13} + 2 q^{14} + q^{16} + 4 q^{17} + q^{18} - q^{19} + O(q^{20})\) 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 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.