Properties

Label 298816.by
Number of curves $2$
Conductor $298816$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("by1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 298816.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
298816.by1 298816by2 \([0, -1, 0, -23553, -23551]\) \(5512402554625/3188422748\) \(835825892851712\) \([2]\) \(1032192\) \(1.5528\)  
298816.by2 298816by1 \([0, -1, 0, 5887, -5887]\) \(86058173375/49827568\) \(-13061997985792\) \([2]\) \(516096\) \(1.2062\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 298816.by have rank \(1\).

Complex multiplication

The elliptic curves in class 298816.by do not have complex multiplication.

Modular form 298816.2.a.by

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