Properties

Label 18480bo
Number of curves $4$
Conductor $18480$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 18480bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18480.j3 18480bo1 \([0, -1, 0, -2661, -52740]\) \(-130287139815424/2250652635\) \(-36010442160\) \([2]\) \(20736\) \(0.82354\) \(\Gamma_0(N)\)-optimal
18480.j2 18480bo2 \([0, -1, 0, -42756, -3388644]\) \(33766427105425744/9823275\) \(2514758400\) \([2]\) \(41472\) \(1.1701\)  
18480.j4 18480bo3 \([0, -1, 0, 10299, -260424]\) \(7549996227362816/6152409907875\) \(-98438558526000\) \([2]\) \(62208\) \(1.3728\)  
18480.j1 18480bo4 \([0, -1, 0, -49596, -2224980]\) \(52702650535889104/22020583921875\) \(5637269484000000\) \([2]\) \(124416\) \(1.7194\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18480bo have rank \(1\).

Complex multiplication

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

Modular form 18480.2.a.bo

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + q^{11} + 2q^{13} + q^{15} - 6q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.