Properties

Label 379050.cw
Number of curves $2$
Conductor $379050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cw1")
 
E.isogeny_class()
 

Elliptic curves in class 379050.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.cw1 379050cw2 \([1, 0, 1, -1060151, 420056858]\) \(-14600882119157955625/14450688\) \(-130417459200\) \([]\) \(3265920\) \(1.8577\)  
379050.cw2 379050cw1 \([1, 0, 1, -12776, 604118]\) \(-25551261405625/2744515872\) \(-24769255744800\) \([]\) \(1088640\) \(1.3084\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 379050.cw have rank \(1\).

Complex multiplication

The elliptic curves in class 379050.cw do not have complex multiplication.

Modular form 379050.2.a.cw

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - 3 q^{11} + q^{12} - 4 q^{13} + q^{14} + q^{16} + 3 q^{17} - q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.