Properties

Label 346560.g
Number of curves $2$
Conductor $346560$
CM no
Rank $1$
Graph

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

Elliptic curves in class 346560.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346560.g1 346560g2 \([0, -1, 0, -2917361, -1291734639]\) \(519388144/164025\) \(867186272308436582400\) \([2]\) \(14008320\) \(2.7217\)  
346560.g2 346560g1 \([0, -1, 0, 512139, -137364939]\) \(44957696/50625\) \(-16728130252863360000\) \([2]\) \(7004160\) \(2.3751\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 346560.g have rank \(1\).

Complex multiplication

The elliptic curves in class 346560.g do not have complex multiplication.

Modular form 346560.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 4 q^{7} + q^{9} + 4 q^{13} + q^{15} - 2 q^{17} + O(q^{20})\) 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.