Properties

Label 51600.cu
Number of curves $2$
Conductor $51600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.cu1 51600bg2 \([0, 1, 0, -248, 708]\) \(13231796/5547\) \(710016000\) \([2]\) \(18432\) \(0.39539\)  
51600.cu2 51600bg1 \([0, 1, 0, 52, 108]\) \(476656/387\) \(-12384000\) \([2]\) \(9216\) \(0.048819\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 51600.cu have rank \(0\).

Complex multiplication

The elliptic curves in class 51600.cu do not have complex multiplication.

Modular form 51600.2.a.cu

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