Properties

Label 1232i
Number of curves $2$
Conductor $1232$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1232i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1232.a2 1232i1 \([0, 1, 0, 56, -588]\) \(4657463/41503\) \(-169996288\) \([2]\) \(384\) \(0.26055\) \(\Gamma_0(N)\)-optimal
1232.a1 1232i2 \([0, 1, 0, -824, -8684]\) \(15124197817/1294139\) \(5300793344\) \([2]\) \(768\) \(0.60713\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1232i have rank \(1\).

Complex multiplication

The elliptic curves in class 1232i do not have complex multiplication.

Modular form 1232.2.a.i

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 2 q^{5} + q^{7} + q^{9} - q^{11} + 4 q^{13} + 4 q^{15} + 4 q^{17} + O(q^{20})\) 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 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.