Properties

Label 18032ba
Number of curves $2$
Conductor $18032$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18032ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18032.v2 18032ba1 \([0, -1, 0, 27032, 8037744]\) \(4533086375/60669952\) \(-29236261612945408\) \([2]\) \(129024\) \(1.8403\) \(\Gamma_0(N)\)-optimal
18032.v1 18032ba2 \([0, -1, 0, -474728, 118023536]\) \(24553362849625/1755162752\) \(845795912130756608\) \([2]\) \(258048\) \(2.1869\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18032ba have rank \(0\).

Complex multiplication

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

Modular form 18032.2.a.ba

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{9} - 4q^{11} - 6q^{17} - 6q^{19} + O(q^{20})\)  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.