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Properties

Label 488410bu
Number of curves $2$
Conductor $488410$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bu1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 488410bu have rank \(1\).

Complex multiplication

The elliptic curves in class 488410bu do not have complex multiplication.

Modular form 488410.2.a.bu

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} + q^{5} - 3 q^{6} + 4 q^{7} + q^{8} + 6 q^{9} + q^{10} - 2 q^{11} - 3 q^{12} + 4 q^{14} - 3 q^{15} + q^{16} + 6 q^{18} + 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 488410bu

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
488410.bu2 488410bu1 \([1, -1, 1, -6798057, 10042351401]\) \(-60698457/40960\) \(-23445546171048266670080\) \([]\) \(99290880\) \(2.9930\) \(\Gamma_0(N)\)-optimal
488410.bu1 488410bu2 \([1, -1, 1, -6159298827, -186063729936171]\) \(-45145776875761017/2441406250\) \(-1397463451090351740722656250\) \([]\) \(1290781440\) \(4.2755\)