Properties

Label 1805.a
Number of curves $2$
Conductor $1805$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1805.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1805.a1 1805a2 \([0, 1, 1, -105171, -9810339]\) \(7575076864/1953125\) \(33171021564453125\) \([]\) \(14364\) \(1.8793\)  
1805.a2 1805a1 \([0, 1, 1, -36581, 2679900]\) \(318767104/125\) \(2122945380125\) \([3]\) \(4788\) \(1.3300\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1805.a have rank \(1\).

Complex multiplication

The elliptic curves in class 1805.a do not have complex multiplication.

Modular form 1805.2.a.a

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - 2 q^{4} - q^{5} - 4 q^{7} + q^{9} + 3 q^{11} + 4 q^{12} + 2 q^{13} + 2 q^{15} + 4 q^{16} + 6 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.