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Properties

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

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

Elliptic curves in class 4018.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4018.i1 4018g2 \([1, 1, 0, -33664887, -75117062635]\) \(35864681248144538691049/43574618474283008\) \(5126510288880921608192\) \([2]\) \(783360\) \(3.0760\)  
4018.i2 4018g1 \([1, 1, 0, -1552247, -1803905515]\) \(-3515753329334380009/9905620513718272\) \(-1165386347818440982528\) \([2]\) \(391680\) \(2.7294\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 4018.i do not have complex multiplication.

Modular form 4018.2.a.i

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