Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 379050x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.x2 379050x1 \([1, 1, 0, -8470150, 12100052500]\) \(-13328910811/4838400\) \(-24395189952092400000000\) \([2]\) \(39398400\) \(3.0062\) \(\Gamma_0(N)\)-optimal
379050.x1 379050x2 \([1, 1, 0, -145650150, 676462792500]\) \(67772591234011/5715360\) \(28816818130909147500000\) \([2]\) \(78796800\) \(3.3528\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 379050.2.a.x

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