Properties

Label 1152.r
Number of curves $2$
Conductor $1152$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1152.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.r1 1152f2 \([0, 0, 0, -84, 272]\) \(10976\) \(5971968\) \([2]\) \(192\) \(0.039450\)  
1152.r2 1152f1 \([0, 0, 0, 6, 20]\) \(128\) \(-186624\) \([2]\) \(96\) \(-0.30712\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1152.r have rank \(0\).

Complex multiplication

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

Modular form 1152.2.a.r

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.