Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 379050y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.y1 379050y1 \([1, 1, 0, -164775, -25797375]\) \(4616586342451/3307500\) \(354470976562500\) \([2]\) \(3317760\) \(1.7271\) \(\Gamma_0(N)\)-optimal
379050.y2 379050y2 \([1, 1, 0, -131525, -36470625]\) \(-2347864201171/3986718750\) \(-427264123535156250\) \([2]\) \(6635520\) \(2.0737\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 379050.2.a.y

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