Properties

Label 1152.e
Number of curves $2$
Conductor $1152$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 1152.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.e1 1152d2 \([0, 0, 0, -36, -80]\) \(23328\) \(221184\) \([2]\) \(128\) \(-0.21042\)  
1152.e2 1152d1 \([0, 0, 0, -6, 4]\) \(3456\) \(6912\) \([2]\) \(64\) \(-0.55700\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1152.e have rank \(1\).

Complex multiplication

The elliptic curves in class 1152.e do not have complex multiplication.

Modular form 1152.2.a.e

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 2 q^{7} + 4 q^{11} + 2 q^{13} - 4 q^{17} + 4 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.