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Properties

Label 301665g
Number of curves $2$
Conductor $301665$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 301665g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301665.g2 301665g1 \([1, 1, 1, -1271, -116836]\) \(-47045881/1183455\) \(-5712311245095\) \([2]\) \(580608\) \(1.1284\) \(\Gamma_0(N)\)-optimal
301665.g1 301665g2 \([1, 1, 1, -44366, -3598912]\) \(2000852317801/10558275\) \(50962776794475\) \([2]\) \(1161216\) \(1.4750\)  

Rank

sage: E.rank()
 

The elliptic curves in class 301665g have rank \(1\).

Complex multiplication

The elliptic curves in class 301665g do not have complex multiplication.

Modular form 301665.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{7} + 3 q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} - q^{14} + q^{15} - q^{16} + q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.