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Properties

Label 4002.g
Number of curves $2$
Conductor $4002$
CM no
Rank $0$
Graph

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

Elliptic curves in class 4002.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4002.g1 4002e2 \([1, 0, 1, -225504, -41235956]\) \(1268188156752269618809/22367178\) \(22367178\) \([2]\) \(15360\) \(1.4027\)  
4002.g2 4002e1 \([1, 0, 1, -14094, -645236]\) \(-309586644846318169/41118653052\) \(-41118653052\) \([2]\) \(7680\) \(1.0561\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4002.g have rank \(0\).

Complex multiplication

The elliptic curves in class 4002.g do not have complex multiplication.

Modular form 4002.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 4 q^{5} - q^{6} - q^{8} + q^{9} - 4 q^{10} + q^{12} - 2 q^{13} + 4 q^{15} + q^{16} + 4 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.