Properties

Label 346800.gg
Number of curves $2$
Conductor $346800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gg1")
 
E.isogeny_class()
 

Elliptic curves in class 346800.gg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346800.gg1 346800gg2 \([0, 1, 0, -15042336808, 710097542878388]\) \(-843137281012581793/216\) \(-96432870864384000000\) \([]\) \(299811456\) \(4.1170\)  
346800.gg2 346800gg1 \([0, 1, 0, -185424808, 977133118388]\) \(-1579268174113/10077696\) \(-4499172023048699904000000\) \([]\) \(99937152\) \(3.5677\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 346800.gg have rank \(0\).

Complex multiplication

The elliptic curves in class 346800.gg do not have complex multiplication.

Modular form 346800.2.a.gg

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4 q^{7} + q^{9} - 3 q^{11} - 2 q^{13} - 8 q^{19} + O(q^{20})\) 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 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.