Properties

Label 4368.g
Number of curves $2$
Conductor $4368$
CM no
Rank $0$
Graph

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

Elliptic curves in class 4368.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4368.g1 4368e2 \([0, -1, 0, -2668, 32656]\) \(8207369602000/3046751253\) \(779968320768\) \([2]\) \(3584\) \(0.98183\)  
4368.g2 4368e1 \([0, -1, 0, 517, 3354]\) \(953312000000/887416803\) \(-14198668848\) \([2]\) \(1792\) \(0.63526\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4368.g have rank \(0\).

Complex multiplication

The elliptic curves in class 4368.g do not have complex multiplication.

Modular form 4368.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + 2 q^{11} - q^{13} - 2 q^{17} + O(q^{20})\) 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.