Properties

Label 254100.y
Number of curves $2$
Conductor $254100$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 254100.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254100.y1 254100y2 \([0, -1, 0, -15331708, 13288921912]\) \(449955166736/174330387\) \(154418457362053500000000\) \([2]\) \(32256000\) \(3.1484\)  
254100.y2 254100y1 \([0, -1, 0, 3045167, 1490968162]\) \(56409309184/50014503\) \(-2768866967161968750000\) \([2]\) \(16128000\) \(2.8018\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 254100.y have rank \(0\).

Complex multiplication

The elliptic curves in class 254100.y do not have complex multiplication.

Modular form 254100.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{7} + q^{9} + 6 q^{13} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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.