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Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 1152j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.s1 1152j1 \([0, 0, 0, -318, -2180]\) \(19056256/27\) \(5038848\) \([2]\) \(384\) \(0.18920\) \(\Gamma_0(N)\)-optimal
1152.s2 1152j2 \([0, 0, 0, -228, -3440]\) \(-219488/729\) \(-4353564672\) \([2]\) \(768\) \(0.53578\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1152.2.a.j

sage: E.q_eigenform(10)
 
\(q + 4 q^{5} - 2 q^{7} + 4 q^{11} + 2 q^{13} + 2 q^{17} - 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.