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Properties

Label 11466.cj
Number of curves $4$
Conductor $11466$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cj1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 11466.cj have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1\)
\(7\)\(1\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - 2 T + 5 T^{2}\) 1.5.ac
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 8 T + 19 T^{2}\) 1.19.ai
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 6 T + 29 T^{2}\) 1.29.g
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 11466.cj do not have complex multiplication.

Modular form 11466.2.a.cj

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 11466.cj

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11466.cj1 11466bz4 \([1, -1, 1, -9146129, 10648717265]\) \(986551739719628473/111045168\) \(9523913315153328\) \([2]\) \(368640\) \(2.4903\)  
11466.cj2 11466bz3 \([1, -1, 1, -1031729, -136548079]\) \(1416134368422073/725251155408\) \(62201978350112332368\) \([2]\) \(368640\) \(2.4903\)  
11466.cj3 11466bz2 \([1, -1, 1, -573089, 165603953]\) \(242702053576633/2554695936\) \(219106360765184256\) \([2, 2]\) \(184320\) \(2.1438\)  
11466.cj4 11466bz1 \([1, -1, 1, -8609, 6420593]\) \(-822656953/207028224\) \(-17756007709999104\) \([2]\) \(92160\) \(1.7972\) \(\Gamma_0(N)\)-optimal