Properties

Label 18032q
Number of curves $2$
Conductor $18032$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 18032q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18032.k2 18032q1 \([0, 0, 0, -7987, -318990]\) \(-116930169/23552\) \(-11349480439808\) \([2]\) \(34560\) \(1.2276\) \(\Gamma_0(N)\)-optimal
18032.k1 18032q2 \([0, 0, 0, -133427, -18758670]\) \(545138290809/16928\) \(8157439066112\) \([2]\) \(69120\) \(1.5742\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18032q have rank \(1\).

Complex multiplication

The elliptic curves in class 18032q do not have complex multiplication.

Modular form 18032.2.a.q

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} - 3 q^{9} - 2 q^{11} + 2 q^{13} + 2 q^{17} - 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.