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Properties

Label 4410.bb
Number of curves $2$
Conductor $4410$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4410.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.bb1 4410w2 \([1, -1, 1, -16148, -785753]\) \(68971442301/400\) \(2700507600\) \([2]\) \(6144\) \(0.99993\)  
4410.bb2 4410w1 \([1, -1, 1, -1028, -11609]\) \(17779581/1280\) \(8641624320\) \([2]\) \(3072\) \(0.65336\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4410.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 4410.bb do not have complex multiplication.

Modular form 4410.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 2 q^{11} - 2 q^{13} + q^{16} - 2 q^{17} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.