Properties

Label 5780.f
Number of curves $4$
Conductor $5780$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5780.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5780.f1 5780e3 \([0, -1, 0, -11945, -498418]\) \(488095744/125\) \(48275138000\) \([2]\) \(6912\) \(1.0360\)  
5780.f2 5780e4 \([0, -1, 0, -10500, -625000]\) \(-20720464/15625\) \(-96550276000000\) \([2]\) \(13824\) \(1.3825\)  
5780.f3 5780e1 \([0, -1, 0, -385, 2130]\) \(16384/5\) \(1931005520\) \([2]\) \(2304\) \(0.48666\) \(\Gamma_0(N)\)-optimal
5780.f4 5780e2 \([0, -1, 0, 1060, 13112]\) \(21296/25\) \(-154480441600\) \([2]\) \(4608\) \(0.83323\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5780.f have rank \(1\).

Complex multiplication

The elliptic curves in class 5780.f do not have complex multiplication.

Modular form 5780.2.a.f

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{5} - 2q^{7} + q^{9} + 2q^{13} + 2q^{15} - 4q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.