Properties

Label 126400.by
Number of curves $3$
Conductor $126400$
CM no
Rank $0$
Graph

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

Elliptic curves in class 126400.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
126400.by1 126400q3 \([0, 1, 0, -8346433, -9283872737]\) \(15698803397448457/20709376\) \(84825604096000000\) \([]\) \(2488320\) \(2.5243\)  
126400.by2 126400q2 \([0, 1, 0, -130433, -5480737]\) \(59914169497/31554496\) \(129247215616000000\) \([]\) \(829440\) \(1.9750\)  
126400.by3 126400q1 \([0, 1, 0, -74433, 7791263]\) \(11134383337/316\) \(1294336000000\) \([]\) \(276480\) \(1.4257\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 126400.by have rank \(0\).

Complex multiplication

The elliptic curves in class 126400.by do not have complex multiplication.

Modular form 126400.2.a.by

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} - 2 q^{9} + 5 q^{13} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.