Properties

Label 8190d
Number of curves $2$
Conductor $8190$
CM no
Rank $1$
Graph

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

Elliptic curves in class 8190d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8190.m1 8190d1 \([1, -1, 0, -1029, -2047]\) \(4465226119563/2499087500\) \(67475362500\) \([2]\) \(7680\) \(0.76814\) \(\Gamma_0(N)\)-optimal
8190.m2 8190d2 \([1, -1, 0, 4041, -19285]\) \(270250212973077/161738281250\) \(-4366933593750\) \([2]\) \(15360\) \(1.1147\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8190d have rank \(1\).

Complex multiplication

The elliptic curves in class 8190d do not have complex multiplication.

Modular form 8190.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + q^{13} + q^{14} + q^{16} - 4 q^{17} - 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.