Properties

Label 19600by
Number of curves $2$
Conductor $19600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 19600by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.ed1 19600by1 \([0, 0, 0, -2581075, -1596064750]\) \(-5154200289/20\) \(-7378945280000000\) \([]\) \(483840\) \(2.2580\) \(\Gamma_0(N)\)-optimal
19600.ed2 19600by2 \([0, 0, 0, 17998925, 15143707250]\) \(1747829720511/1280000000\) \(-472252497920000000000000\) \([]\) \(3386880\) \(3.2310\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19600by have rank \(0\).

Complex multiplication

The elliptic curves in class 19600by do not have complex multiplication.

Modular form 19600.2.a.by

sage: E.q_eigenform(10)
 
\(q + 3 q^{3} + 6 q^{9} + 2 q^{11} + 4 q^{17} + 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.