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Properties

Label 84474.by
Number of curves $2$
Conductor $84474$
CM no
Rank $1$
Graph

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

Elliptic curves in class 84474.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84474.by1 84474ce2 \([1, -1, 1, -691022, -242412713]\) \(-1064019559329/125497034\) \(-4304102406486959466\) \([]\) \(1284192\) \(2.3113\)  
84474.by2 84474ce1 \([1, -1, 1, -8732, 482527]\) \(-2146689/1664\) \(-57069288222336\) \([]\) \(183456\) \(1.3384\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 84474.by have rank \(1\).

Complex multiplication

The elliptic curves in class 84474.by do not have complex multiplication.

Modular form 84474.2.a.by

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} + 2 q^{11} + q^{13} + q^{14} + q^{16} + 3 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.