Properties

Label 17600.bb
Number of curves $3$
Conductor $17600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 17600.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17600.bb1 17600w3 \([0, -1, 0, -48524833, 130122917537]\) \(-24680042791780949/369098752\) \(-188978561024000000000\) \([]\) \(1152000\) \(3.0276\)  
17600.bb2 17600w1 \([0, -1, 0, -44833, -3642463]\) \(-19465109/22\) \(-11264000000000\) \([]\) \(46080\) \(1.4181\) \(\Gamma_0(N)\)-optimal
17600.bb3 17600w2 \([0, -1, 0, 315167, 38237537]\) \(6761990971/5153632\) \(-2638659584000000000\) \([]\) \(230400\) \(2.2228\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17600.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 17600.bb do not have complex multiplication.

Modular form 17600.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{7} - 2 q^{9} - q^{11} + 4 q^{13} - 3 q^{17} + 5 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrr} 1 & 25 & 5 \\ 25 & 1 & 5 \\ 5 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.