Properties

Label 138720bl
Number of curves $4$
Conductor $138720$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 138720bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
138720.o3 138720bl1 \([0, -1, 0, -1830, 10800]\) \(438976/225\) \(347580993600\) \([2, 2]\) \(163840\) \(0.90676\) \(\Gamma_0(N)\)-optimal
138720.o1 138720bl2 \([0, -1, 0, -23505, 1393665]\) \(14526784/15\) \(1483012239360\) \([2]\) \(327680\) \(1.2533\)  
138720.o4 138720bl3 \([0, -1, 0, 6840, 76692]\) \(2863288/1875\) \(-23172066240000\) \([2]\) \(327680\) \(1.2533\)  
138720.o2 138720bl4 \([0, -1, 0, -16280, -786840]\) \(38614472/405\) \(5005166307840\) \([2]\) \(327680\) \(1.2533\)  

Rank

sage: E.rank()
 

The elliptic curves in class 138720bl have rank \(0\).

Complex multiplication

The elliptic curves in class 138720bl do not have complex multiplication.

Modular form 138720.2.a.bl

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

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.