Properties

Label 254100by
Number of curves $2$
Conductor $254100$
CM no
Rank $2$
Graph

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

Elliptic curves in class 254100by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254100.by2 254100by1 \([0, 1, 0, -64533, -19807812]\) \(-67108864/343035\) \(-151926856908750000\) \([2]\) \(2764800\) \(1.9812\) \(\Gamma_0(N)\)-optimal
254100.by1 254100by2 \([0, 1, 0, -1561908, -750526812]\) \(59466754384/121275\) \(859384241100000000\) \([2]\) \(5529600\) \(2.3277\)  

Rank

sage: E.rank()
 

The elliptic curves in class 254100by have rank \(2\).

Complex multiplication

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

Modular form 254100.2.a.by

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