Properties

Label 1155.e
Number of curves $6$
Conductor $1155$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1155.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.e1 1155e5 \([1, 1, 1, -13250, -592540]\) \(257260669489908001/14267882475\) \(14267882475\) \([2]\) \(2048\) \(1.0139\)  
1155.e2 1155e3 \([1, 1, 1, -875, -8440]\) \(74093292126001/14707625625\) \(14707625625\) \([2, 2]\) \(1024\) \(0.66729\)  
1155.e3 1155e2 \([1, 1, 1, -270, 1482]\) \(2177286259681/161417025\) \(161417025\) \([2, 4]\) \(512\) \(0.32072\)  
1155.e4 1155e1 \([1, 1, 1, -265, 1550]\) \(2058561081361/12705\) \(12705\) \([4]\) \(256\) \(-0.025854\) \(\Gamma_0(N)\)-optimal
1155.e5 1155e4 \([1, 1, 1, 255, 7152]\) \(1833318007919/22507682505\) \(-22507682505\) \([4]\) \(1024\) \(0.66729\)  
1155.e6 1155e6 \([1, 1, 1, 1820, -47248]\) \(666688497209279/1381398046875\) \(-1381398046875\) \([2]\) \(2048\) \(1.0139\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1155.e have rank \(1\).

Complex multiplication

The elliptic curves in class 1155.e do not have complex multiplication.

Modular form 1155.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} - q^{7} + 3 q^{8} + q^{9} - q^{10} + q^{11} + q^{12} - 2 q^{13} + q^{14} - q^{15} - q^{16} - 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

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

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

The vertices are labelled with LMFDB labels.