Properties

Label 5390.i
Number of curves $4$
Conductor $5390$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5390.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5390.i1 5390c4 \([1, -1, 0, -160066790, 779511027056]\) \(3855131356812007128171561/8967612500\) \(1055030643012500\) \([2]\) \(491520\) \(3.0130\)  
5390.i2 5390c3 \([1, -1, 0, -10532510, 10824019800]\) \(1098325674097093229481/205612182617187500\) \(24190067672729492187500\) \([2]\) \(491520\) \(3.0130\)  
5390.i3 5390c2 \([1, -1, 0, -10004290, 12181439556]\) \(941226862950447171561/45393906250000\) \(5340547676406250000\) \([2, 2]\) \(245760\) \(2.6664\)  
5390.i4 5390c1 \([1, -1, 0, -592370, 211359700]\) \(-195395722614328041/50730248800000\) \(-5968363041071200000\) \([2]\) \(122880\) \(2.3198\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5390.i have rank \(0\).

Complex multiplication

The elliptic curves in class 5390.i do not have complex multiplication.

Modular form 5390.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} - 3 q^{9} + q^{10} - q^{11} - 2 q^{13} + q^{16} - 6 q^{17} + 3 q^{18} - 4 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.