Properties

Label 93600.cp
Number of curves $4$
Conductor $93600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 93600.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93600.cp1 93600dt4 \([0, 0, 0, -234300, 43652000]\) \(30488290624/195\) \(9097920000000\) \([4]\) \(294912\) \(1.6712\)  
93600.cp2 93600dt3 \([0, 0, 0, -48675, -3361750]\) \(2186875592/428415\) \(2498516280000000\) \([2]\) \(294912\) \(1.6712\)  
93600.cp3 93600dt1 \([0, 0, 0, -14925, 654500]\) \(504358336/38025\) \(27720225000000\) \([2, 2]\) \(147456\) \(1.3247\) \(\Gamma_0(N)\)-optimal
93600.cp4 93600dt2 \([0, 0, 0, 14325, 2906750]\) \(55742968/658125\) \(-3838185000000000\) \([2]\) \(294912\) \(1.6712\)  

Rank

sage: E.rank()
 

The elliptic curves in class 93600.cp have rank \(0\).

Complex multiplication

The elliptic curves in class 93600.cp do not have complex multiplication.

Modular form 93600.2.a.cp

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.