Properties

Label 235200k
Number of curves $2$
Conductor $235200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235200k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.k2 235200k1 \([0, -1, 0, 1919167, 82569537]\) \(2595575/1512\) \(-455386337280000000000\) \([]\) \(9953280\) \(2.6534\) \(\Gamma_0(N)\)-optimal
235200.k1 235200k2 \([0, -1, 0, -27480833, 58676769537]\) \(-7620530425/526848\) \(-158676839301120000000000\) \([]\) \(29859840\) \(3.2027\)  

Rank

sage: E.rank()
 

The elliptic curves in class 235200k have rank \(0\).

Complex multiplication

The elliptic curves in class 235200k do not have complex multiplication.

Modular form 235200.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 6q^{11} + q^{13} + 3q^{17} - 4q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.