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Properties

Label 354025.k
Number of curves $2$
Conductor $354025$
CM no
Rank $2$
Graph

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

Elliptic curves in class 354025.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
354025.k1 354025k2 \([1, 1, 1, -2946663658, 61565201177556]\) \(-162677523113838677\) \(-17393535238596125\) \([]\) \(63651840\) \(3.6600\)  
354025.k2 354025k1 \([1, 1, 1, -113583, -16089494]\) \(-9317\) \(-17393535238596125\) \([]\) \(1720320\) \(1.8546\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 354025.k have rank \(2\).

Complex multiplication

The elliptic curves in class 354025.k do not have complex multiplication.

Modular form 354025.2.a.k

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

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.