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Properties

Label 388080x
Number of curves $4$
Conductor $388080$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("x1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 388080x have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1 + T\)
\(7\)\(1\)
\(11\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 8 T + 23 T^{2}\) 1.23.i
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 388080.2.a.x

Copy content sage:E.q_eigenform(10)
 
\(q - q^{5} - q^{11} - 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 388080x

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.x3 388080x1 \([0, 0, 0, -1737079743, -27865736983042]\) \(26401417552259125806544/507547744790625\) \(11143782731005405034400000\) \([2]\) \(188743680\) \(3.9291\) \(\Gamma_0(N)\)-optimal
388080.x2 388080x2 \([0, 0, 0, -1794947763, -25909786333438]\) \(7282213870869695463556/912102595400390625\) \(80104961599000520490000000000\) \([2, 2]\) \(377487360\) \(4.2756\)  
388080.x1 388080x3 \([0, 0, 0, -7185961083, 207660178566218]\) \(233632133015204766393938/29145526885986328125\) \(5119383112729101562500000000000\) \([2]\) \(754974720\) \(4.6222\)  
388080.x4 388080x4 \([0, 0, 0, 2670177237, -134298909658438]\) \(11986661998777424518222/51295853620928503125\) \(-9010066203547324685040902400000\) \([2]\) \(754974720\) \(4.6222\)