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Properties

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

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Show commands: SageMath
E = EllipticCurve("gz1")
 
E.isogeny_class()
 

Elliptic curves in class 379050gz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.gz1 379050gz1 \([1, 1, 1, -589359763, -5527288442719]\) \(-1231922871794037145/5186378855952\) \(-95311625967982005356250000\) \([]\) \(186624000\) \(3.8397\) \(\Gamma_0(N)\)-optimal
379050.gz2 379050gz2 \([1, 1, 1, 1378315862, -29142405328969]\) \(15757536948921630455/29083977048526848\) \(-534484891887392701684800000000\) \([]\) \(559872000\) \(4.3890\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 379050.2.a.gz

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