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Properties

Label 4080i
Number of curves $2$
Conductor $4080$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4080i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4080.k2 4080i1 \([0, -1, 0, 80, 400]\) \(54607676/108375\) \(-110976000\) \([2]\) \(1152\) \(0.22822\) \(\Gamma_0(N)\)-optimal
4080.k1 4080i2 \([0, -1, 0, -600, 4752]\) \(11683450802/2390625\) \(4896000000\) \([2]\) \(2304\) \(0.57479\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4080i have rank \(1\).

Complex multiplication

The elliptic curves in class 4080i do not have complex multiplication.

Modular form 4080.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 2 q^{7} + q^{9} - 4 q^{11} + 4 q^{13} - q^{15} + q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.