Properties

Label 23232i
Number of curves $4$
Conductor $23232$
CM no
Rank $0$
Graph

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

Elliptic curves in class 23232i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23232.s3 23232i1 \([0, -1, 0, -42753, -3195135]\) \(18609625/1188\) \(551712055099392\) \([2]\) \(92160\) \(1.5793\) \(\Gamma_0(N)\)-optimal
23232.s4 23232i2 \([0, -1, 0, 34687, -13556607]\) \(9938375/176418\) \(-81929240182259712\) \([2]\) \(184320\) \(1.9259\)  
23232.s1 23232i3 \([0, -1, 0, -623553, 189003201]\) \(57736239625/255552\) \(118679393185824768\) \([2]\) \(276480\) \(2.1286\)  
23232.s2 23232i4 \([0, -1, 0, -313793, 376531905]\) \(-7357983625/127552392\) \(-59235852123874787328\) \([2]\) \(552960\) \(2.4752\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23232i have rank \(0\).

Complex multiplication

The elliptic curves in class 23232i do not have complex multiplication.

Modular form 23232.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{7} + q^{9} - 4 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.