Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1152.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1152.i1 1152r2 [0, 0, 0, -120, -416] [2] 256  
1152.i2 1152r1 [0, 0, 0, 15, -38] [2] 128 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1152.2.a.i

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

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.