Properties

Label 51600.y
Number of curves $4$
Conductor $51600$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.y1 51600bz4 \([0, -1, 0, -275408, -55538688]\) \(36097320816649/80625\) \(5160000000000\) \([2]\) \(270336\) \(1.6845\)  
51600.y2 51600bz3 \([0, -1, 0, -47408, 2877312]\) \(184122897769/51282015\) \(3282048960000000\) \([4]\) \(270336\) \(1.6845\)  
51600.y3 51600bz2 \([0, -1, 0, -17408, -842688]\) \(9116230969/416025\) \(26625600000000\) \([2, 2]\) \(135168\) \(1.3379\)  
51600.y4 51600bz1 \([0, -1, 0, 592, -50688]\) \(357911/17415\) \(-1114560000000\) \([2]\) \(67584\) \(0.99136\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 51600.2.a.y

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.