Properties

Label 51600.cl
Number of curves $2$
Conductor $51600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.cl1 51600cu2 \([0, 1, 0, -95008, 10879988]\) \(1481933914201/53916840\) \(3450677760000000\) \([2]\) \(331776\) \(1.7512\)  
51600.cl2 51600cu1 \([0, 1, 0, -15008, -480012]\) \(5841725401/1857600\) \(118886400000000\) \([2]\) \(165888\) \(1.4046\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 51600.cl have rank \(1\).

Complex multiplication

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

Modular form 51600.2.a.cl

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{7} + q^{9} + 2q^{11} + 2q^{13} + 4q^{17} + 6q^{19} + O(q^{20})\)  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.