Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1152.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.k1 1152p1 \([0, 0, 0, -30, 52]\) \(16000/3\) \(559872\) \([2]\) \(128\) \(-0.17914\) \(\Gamma_0(N)\)-optimal
1152.k2 1152p2 \([0, 0, 0, 60, 304]\) \(4000/9\) \(-53747712\) \([2]\) \(256\) \(0.16743\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1152.2.a.k

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} - 4 q^{11} - 6 q^{13} - 6 q^{17} + O(q^{20})\) 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.