Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19600u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.de2 19600u1 \([0, -1, 0, 992, -13488]\) \(19652/25\) \(-137200000000\) \([2]\) \(18432\) \(0.82304\) \(\Gamma_0(N)\)-optimal
19600.de1 19600u2 \([0, -1, 0, -6008, -125488]\) \(2185454/625\) \(6860000000000\) \([2]\) \(36864\) \(1.1696\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 19600.2.a.u

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{9} - 4 q^{11} - 2 q^{13} - 2 q^{19} + O(q^{20})\) 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 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.