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Properties

Label 4002.b
Number of curves $2$
Conductor $4002$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 4002.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4002.b1 4002a2 \([1, 1, 0, -270, 1458]\) \(2189403771625/201304602\) \(201304602\) \([2]\) \(1792\) \(0.33231\)  
4002.b2 4002a1 \([1, 1, 0, 20, 124]\) \(817400375/6267132\) \(-6267132\) \([2]\) \(896\) \(-0.014264\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4002.b have rank \(1\).

Complex multiplication

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

Modular form 4002.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{12} + 6 q^{13} + 4 q^{14} + q^{16} - q^{18} + O(q^{20})\) 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.