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Properties

Label 390390y
Number of curves $4$
Conductor $390390$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("y1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 390390y have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 + T\)
\(5\)\(1 - T\)
\(7\)\(1 - T\)
\(11\)\(1 + T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 390390y do not have complex multiplication.

Modular form 390390.2.a.y

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} - q^{11} - q^{12} - q^{14} - q^{15} + q^{16} - 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 390390y

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
390390.y4 390390y1 \([1, 1, 0, -257323797, -4458583836819]\) \(-390394287570401650575649/1553162059549900800000\) \(-7496816607493997130547200000\) \([2]\) \(309657600\) \(4.0341\) \(\Gamma_0(N)\)-optimal
390390.y3 390390y2 \([1, 1, 0, -5934425877, -175710638920851]\) \(4788502600127122071579248929/7954695558810000000000\) \(38395796115524137290000000000\) \([2, 2]\) \(619315200\) \(4.3806\)  
390390.y2 390390y3 \([1, 1, 0, -7789559157, -56641877557299]\) \(10829346205367046227129003809/5979872213745117187500000\) \(28863701020154855346679687500000\) \([2]\) \(1238630400\) \(4.7272\)  
390390.y1 390390y4 \([1, 1, 0, -94912925877, -11254797383620851]\) \(19590236683225255317943875248929/54195348396489300000\) \(261590595398310121643700000\) \([2]\) \(1238630400\) \(4.7272\)