Properties

Label 235200bbi
Number of curves $4$
Conductor $235200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bbi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235200bbi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.bbi3 235200bbi1 [0, 1, 0, -276033, 35148063] [2] 3538944 \(\Gamma_0(N)\)-optimal
235200.bbi2 235200bbi2 [0, 1, 0, -1844033, -938579937] [2, 2] 7077888  
235200.bbi4 235200bbi3 [0, 1, 0, 507967, -3165923937] [2] 14155776  
235200.bbi1 235200bbi4 [0, 1, 0, -29284033, -61004739937] [2] 14155776  

Rank

sage: E.rank()
 

The elliptic curves in class 235200bbi have rank \(1\).

Complex multiplication

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

Modular form 235200.2.a.bbi

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.