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Properties

Label 1176.i
Number of curves $6$
Conductor $1176$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("i1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 1176.i have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(7\)\(1\)
 
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
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 8 T + 23 T^{2}\) 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 1176.i do not have complex multiplication.

Modular form 1176.2.a.i

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{5} + q^{9} + 4 q^{11} + 2 q^{13} + 2 q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 1176.i

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1176.i1 1176i5 \([0, 1, 0, -18832, 988448]\) \(3065617154/9\) \(2168506368\) \([2]\) \(1536\) \(1.0208\)  
1176.i2 1176i3 \([0, 1, 0, -3152, -69168]\) \(28756228/3\) \(361417728\) \([2]\) \(768\) \(0.67418\)  
1176.i3 1176i4 \([0, 1, 0, -1192, 14720]\) \(1556068/81\) \(9758278656\) \([2, 2]\) \(768\) \(0.67418\)  
1176.i4 1176i2 \([0, 1, 0, -212, -960]\) \(35152/9\) \(271063296\) \([2, 2]\) \(384\) \(0.32760\)  
1176.i5 1176i1 \([0, 1, 0, 33, -78]\) \(2048/3\) \(-5647152\) \([2]\) \(192\) \(-0.018971\) \(\Gamma_0(N)\)-optimal
1176.i6 1176i6 \([0, 1, 0, 768, 60192]\) \(207646/6561\) \(-1580841142272\) \([2]\) \(1536\) \(1.0208\)