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Properties

Label 141120.y
Number of curves $6$
Conductor $141120$
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 141120.y have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1 + T\)
\(7\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 10 T + 29 T^{2}\) 1.29.k
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 141120.y do not have complex multiplication.

Modular form 141120.2.a.y

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 141120.y

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.y1 141120lh6 \([0, 0, 0, -18487308, -30594892048]\) \(62161150998242/1607445\) \(18070152461791395840\) \([2]\) \(6291456\) \(2.8018\)  
141120.y2 141120lh4 \([0, 0, 0, -1200108, -439100368]\) \(34008619684/4862025\) \(27328316994684518400\) \([2, 2]\) \(3145728\) \(2.4552\)  
141120.y3 141120lh2 \([0, 0, 0, -318108, 62228432]\) \(2533446736/275625\) \(387306079856640000\) \([2, 2]\) \(1572864\) \(2.1086\)  
141120.y4 141120lh1 \([0, 0, 0, -309288, 66204488]\) \(37256083456/525\) \(46107866649600\) \([2]\) \(786432\) \(1.7620\) \(\Gamma_0(N)\)-optimal
141120.y5 141120lh3 \([0, 0, 0, 422772, 309089648]\) \(1486779836/8203125\) \(-46107866649600000000\) \([2]\) \(3145728\) \(2.4552\)  
141120.y6 141120lh5 \([0, 0, 0, 1975092, -2368351888]\) \(75798394558/259416045\) \(-2916235071299445719040\) \([2]\) \(6291456\) \(2.8018\)