Properties

Label 79350.k
Number of curves $6$
Conductor $79350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 79350.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
79350.k1 79350e4 \([1, 1, 0, -1460040275, -21473739057375]\) \(148809678420065817601/20700\) \(47880357848437500\) \([2]\) \(19464192\) \(3.5255\)  
79350.k2 79350e6 \([1, 1, 0, -341602025, 2081475474375]\) \(1905890658841300321/293666194803750\) \(679267753390942371621093750\) \([2]\) \(38928384\) \(3.8721\)  
79350.k3 79350e3 \([1, 1, 0, -93633275, -317126244375]\) \(39248884582600321/3935264062500\) \(9102504905342797851562500\) \([2, 2]\) \(19464192\) \(3.5255\)  
79350.k4 79350e2 \([1, 1, 0, -91252775, -335553694875]\) \(36330796409313601/428490000\) \(991123407462656250000\) \([2, 2]\) \(9732096\) \(3.1789\)  
79350.k5 79350e1 \([1, 1, 0, -5554775, -5530696875]\) \(-8194759433281/965779200\) \(-2233905975776700000000\) \([2]\) \(4866048\) \(2.8323\) \(\Gamma_0(N)\)-optimal
79350.k6 79350e5 \([1, 1, 0, 116247475, -1536323521125]\) \(75108181893694559/484313964843750\) \(-1120247630324363708496093750\) \([2]\) \(38928384\) \(3.8721\)  

Rank

sage: E.rank()
 

The elliptic curves in class 79350.k have rank \(0\).

Complex multiplication

The elliptic curves in class 79350.k do not have complex multiplication.

Modular form 79350.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4 q^{11} - q^{12} + 2 q^{13} + q^{16} - 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.