Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1152.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.f1 1152c2 \([0, 0, 0, -216, 864]\) \(3456\) \(322486272\) \([2]\) \(384\) \(0.33888\)  
1152.f2 1152c1 \([0, 0, 0, -81, -270]\) \(23328\) \(2519424\) \([2]\) \(192\) \(-0.0076923\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1152.2.a.f

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