Properties

Label 4018.i
Number of curves 2
Conductor 4018
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4018.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4018.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4018.i1 4018g2 [1, 1, 0, -33664887, -75117062635] [2] 783360  
4018.i2 4018g1 [1, 1, 0, -1552247, -1803905515] [2] 391680 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4018.i have rank \(1\).

Modular form 4018.2.a.i

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

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.