Properties

Label 816.d
Number of curves $4$
Conductor $816$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 816.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
816.d1 816e3 \([0, -1, 0, -12008, 386928]\) \(46753267515625/11591221248\) \(47477642231808\) \([2]\) \(1728\) \(1.3346\)  
816.d2 816e1 \([0, -1, 0, -4088, -99216]\) \(1845026709625/793152\) \(3248750592\) \([2]\) \(576\) \(0.78527\) \(\Gamma_0(N)\)-optimal
816.d3 816e2 \([0, -1, 0, -3448, -131984]\) \(-1107111813625/1228691592\) \(-5032720760832\) \([2]\) \(1152\) \(1.1318\)  
816.d4 816e4 \([0, -1, 0, 28952, 2418544]\) \(655215969476375/1001033261568\) \(-4100232239382528\) \([2]\) \(3456\) \(1.6811\)  

Rank

sage: E.rank()
 

The elliptic curves in class 816.d have rank \(0\).

Complex multiplication

The elliptic curves in class 816.d do not have complex multiplication.

Modular form 816.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.