Properties

Label 51600.dq
Number of curves $4$
Conductor $51600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.dq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.dq1 51600di4 \([0, 1, 0, -2073008, 990587988]\) \(15393836938735081/2275690697640\) \(145644204648960000000\) \([2]\) \(1658880\) \(2.5936\)  
51600.dq2 51600di3 \([0, 1, 0, -1993008, 1082267988]\) \(13679527032530281/381633600\) \(24424550400000000\) \([2]\) \(829440\) \(2.2471\)  
51600.dq3 51600di2 \([0, 1, 0, -543008, -154032012]\) \(276670733768281/336980250\) \(21566736000000000\) \([2]\) \(552960\) \(2.0443\)  
51600.dq4 51600di1 \([0, 1, 0, -43008, -1032012]\) \(137467988281/72562500\) \(4644000000000000\) \([2]\) \(276480\) \(1.6978\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 51600.2.a.dq

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.