Properties

Label 9900bb
Number of curves $2$
Conductor $9900$
CM no
Rank $1$
Graph

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

Elliptic curves in class 9900bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9900.j1 9900bb1 \([0, 0, 0, -1239375, -531076250]\) \(-2888047810000/35937\) \(-2619807300000000\) \([]\) \(103680\) \(2.1056\) \(\Gamma_0(N)\)-optimal
9900.j2 9900bb2 \([0, 0, 0, -564375, -1104691250]\) \(-272709010000/7073843073\) \(-515683160021700000000\) \([3]\) \(311040\) \(2.6549\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9900bb have rank \(1\).

Complex multiplication

The elliptic curves in class 9900bb do not have complex multiplication.

Modular form 9900.2.a.bb

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