Properties

Label 296208.bb
Number of curves $2$
Conductor $296208$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 296208.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
296208.bb1 296208bb2 [0, 0, 0, -3171531, -2173855750] [2] 4423680  
296208.bb2 296208bb1 [0, 0, 0, -209451, -29902246] [2] 2211840 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 296208.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 296208.bb do not have complex multiplication.

Modular form 296208.2.a.bb

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - 2q^{7} - 4q^{13} + q^{17} + 2q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.