Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1152.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1152.l1 1152e2 \([0, 0, 0, -120, 416]\) \(16000/3\) \(35831808\) \([2]\) \(256\) \(0.16743\)  
1152.l2 1152e1 \([0, 0, 0, 15, 38]\) \(4000/9\) \(-839808\) \([2]\) \(128\) \(-0.17914\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1152.2.a.l

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