Properties

Label 235200r
Number of curves $4$
Conductor $235200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("235200.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235200r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.r2 235200r1 [0, -1, 0, -300533, -63151563] [2] 2654208 \(\Gamma_0(N)\)-optimal
235200.r3 235200r2 [0, -1, 0, -178033, -115214063] [2] 5308416  
235200.r1 235200r3 [0, -1, 0, -1476533, 638332437] [2] 7962624  
235200.r4 235200r4 [0, -1, 0, 1585967, 2938269937] [2] 15925248  

Rank

sage: E.rank()
 

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

Modular form 235200.2.a.r

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{9} - 6q^{11} + 4q^{13} + 6q^{17} + 2q^{19} + O(q^{20}) \)

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 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.