Properties

Label 388080.jl
Number of curves $2$
Conductor $388080$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("jl1")
 
E.isogeny_class()
 

Elliptic curves in class 388080.jl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.jl1 388080jl1 \([0, 0, 0, -296352, -40387221]\) \(226492416/75625\) \(961078856363010000\) \([2]\) \(5160960\) \(2.1532\) \(\Gamma_0(N)\)-optimal
388080.jl2 388080jl2 \([0, 0, 0, 861273, -278626446]\) \(347482224/366025\) \(-74425946636751494400\) \([2]\) \(10321920\) \(2.4997\)  

Rank

sage: E.rank()
 

The elliptic curves in class 388080.jl have rank \(0\).

Complex multiplication

The elliptic curves in class 388080.jl do not have complex multiplication.

Modular form 388080.2.a.jl

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{11} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.