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Properties

Label 440440bb
Number of curves $2$
Conductor $440440$
CM no
Rank $0$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 440440bb have rank \(0\).

Complex multiplication

The elliptic curves in class 440440bb do not have complex multiplication.

Modular form 440440.2.a.bb

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

Isogeny matrix

Copy content 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 440440bb

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
440440.bb2 440440bb1 \([0, 0, 0, 40777, 1381578]\) \(16533829296/11386375\) \(-5163944417632000\) \([2]\) \(1658880\) \(1.7036\) \(\Gamma_0(N)\)-optimal*
440440.bb1 440440bb2 \([0, 0, 0, -179443, 11555742]\) \(352246923396/172046875\) \(312106530736000000\) \([2]\) \(3317760\) \(2.0502\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 440440bb1.