Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("ds1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 379050.ds

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.ds1 379050ds2 \([1, 0, 1, -3163451, 2291105798]\) \(-7620530425/526848\) \(-242051057745000000000\) \([]\) \(22394880\) \(2.6623\)  
379050.ds2 379050ds1 \([1, 0, 1, 220924, 3268298]\) \(2595575/1512\) \(-694661836640625000\) \([]\) \(7464960\) \(2.1129\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 379050.2.a.ds

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