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Properties

Label 154154.r
Number of curves $4$
Conductor $154154$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("r1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 154154.r have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(7\)\(1\)
\(11\)\(1\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 + 3 T^{2}\) 1.3.a
\(5\) \( 1 + 2 T + 5 T^{2}\) 1.5.c
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 - 8 T + 23 T^{2}\) 1.23.ai
\(29\) \( 1 - 10 T + 29 T^{2}\) 1.29.ak
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 154154.r do not have complex multiplication.

Modular form 154154.2.a.r

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 154154.r

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154154.r1 154154cb3 \([1, -1, 0, -350603633, 2526043580605]\) \(22868021811807457713/8953460393696\) \(1866101525286715291518944\) \([2]\) \(44236800\) \(3.6219\)  
154154.r2 154154cb4 \([1, -1, 0, -185540273, -953969783299]\) \(3389174547561866673/74853681183008\) \(15601182390585720544327712\) \([2]\) \(44236800\) \(3.6219\)  
154154.r3 154154cb2 \([1, -1, 0, -25220113, 26772763485]\) \(8511781274893233/3440817243136\) \(717143319265676518319104\) \([2, 2]\) \(22118400\) \(3.2753\)  
154154.r4 154154cb1 \([1, -1, 0, 5136367, 3040067421]\) \(71903073502287/60782804992\) \(-12668496884918190604288\) \([2]\) \(11059200\) \(2.9288\) \(\Gamma_0(N)\)-optimal