Properties

Label 10080i
Number of curves $4$
Conductor $10080$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 10080i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10080.j3 10080i1 \([0, 0, 0, -8013, 267388]\) \(1219555693504/43758225\) \(2041583745600\) \([2, 2]\) \(12288\) \(1.1323\) \(\Gamma_0(N)\)-optimal
10080.j2 10080i2 \([0, 0, 0, -20163, -736202]\) \(2428799546888/778248135\) \(290479559892480\) \([2]\) \(24576\) \(1.4789\)  
10080.j1 10080i3 \([0, 0, 0, -127083, 17437282]\) \(608119035935048/826875\) \(308629440000\) \([2]\) \(24576\) \(1.4789\)  
10080.j4 10080i4 \([0, 0, 0, 3012, 946528]\) \(1012048064/130203045\) \(-388784209121280\) \([2]\) \(24576\) \(1.4789\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10080i have rank \(0\).

Complex multiplication

The elliptic curves in class 10080i do not have complex multiplication.

Modular form 10080.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.