Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 379050r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.r1 379050r1 \([1, 1, 0, -726700, -29006000]\) \(461889917/263424\) \(24205105774500000000\) \([2]\) \(12579840\) \(2.4092\) \(\Gamma_0(N)\)-optimal
379050.r2 379050r2 \([1, 1, 0, 2883300, -227556000]\) \(28849701763/16941456\) \(-1556690865122531250000\) \([2]\) \(25159680\) \(2.7558\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 379050.2.a.r

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