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Properties

Label 379050.gm
Number of curves $2$
Conductor $379050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gm1")
 
E.isogeny_class()
 

Elliptic curves in class 379050.gm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.gm1 379050gm2 \([1, 1, 1, -1413503, 643439981]\) \(53110735567469/266050008\) \(1564569627052131000\) \([2]\) \(13271040\) \(2.3382\)  
379050.gm2 379050gm1 \([1, 1, 1, -41703, 20642781]\) \(-1363938029/30566592\) \(-179754031225944000\) \([2]\) \(6635520\) \(1.9916\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 379050.gm have rank \(0\).

Complex multiplication

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

Modular form 379050.2.a.gm

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.