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Properties

Label 18480bb
Number of curves $2$
Conductor $18480$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 18480bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18480.cu1 18480bb1 \([0, 1, 0, -120, -540]\) \(188183524/3465\) \(3548160\) \([2]\) \(4608\) \(0.051452\) \(\Gamma_0(N)\)-optimal
18480.cu2 18480bb2 \([0, 1, 0, 0, -1452]\) \(-2/444675\) \(-910694400\) \([2]\) \(9216\) \(0.39803\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18480bb have rank \(0\).

Complex multiplication

The elliptic curves in class 18480bb do not have complex multiplication.

Modular form 18480.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} + q^{9} + q^{11} + q^{15} + 8 q^{17} - 8 q^{19} + O(q^{20})\) 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.