↑

Properties

Label 436810f
Number of curves $2$
Conductor $436810$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("f1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 436810f have rank \(1\).

Complex multiplication

The elliptic curves in class 436810f do not have complex multiplication.

Modular form 436810.2.a.f

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} - q^{5} + 2 q^{6} - q^{8} + q^{9} + q^{10} - 2 q^{12} + 2 q^{13} + 2 q^{15} + q^{16} + 6 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 436810f

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436810.f2 436810f1 \([1, 0, 1, -1349274, -602568628]\) \(16796884481/25600\) \(414032978241766400\) \([2]\) \(9292800\) \(2.2802\) \(\Gamma_0(N)\)-optimal
436810.f1 436810f2 \([1, 0, 1, -21580474, -38588669748]\) \(68724510023681/160\) \(2587706114011040\) \([2]\) \(18585600\) \(2.6267\)