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Properties

Label 284746k
Number of curves $2$
Conductor $284746$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 284746k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
284746.k2 284746k1 \([1, 0, 0, -26849, 1748665]\) \(-338608873/13552\) \(-85667112040048\) \([2]\) \(1290240\) \(1.4417\) \(\Gamma_0(N)\)-optimal
284746.k1 284746k2 \([1, 0, 0, -433629, 109870789]\) \(1426487591593/2156\) \(13628858733644\) \([2]\) \(2580480\) \(1.7883\)  

Rank

sage: E.rank()
 

The elliptic curves in class 284746k have rank \(1\).

Complex multiplication

The elliptic curves in class 284746k do not have complex multiplication.

Modular form 284746.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + q^{8} + q^{9} - 2 q^{10} + q^{11} - 2 q^{12} - 4 q^{13} + q^{14} + 4 q^{15} + q^{16} + q^{18} - 4 q^{19} + O(q^{20})\) 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.