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Properties

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

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 4002.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4002.m1 4002m1 \([1, 0, 0, -92, 336]\) \(-86175179713/1152576\) \(-1152576\) \([3]\) \(1440\) \(-0.029222\) \(\Gamma_0(N)\)-optimal
4002.m2 4002m2 \([1, 0, 0, 328, 1764]\) \(3901777377407/3560891556\) \(-3560891556\) \([]\) \(4320\) \(0.52008\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4002.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 3 q^{5} + q^{6} - 4 q^{7} + q^{8} + q^{9} - 3 q^{10} + 3 q^{11} + q^{12} + 5 q^{13} - 4 q^{14} - 3 q^{15} + q^{16} - 6 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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.