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Properties

Label 436810l
Number of curves $2$
Conductor $436810$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("l1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 436810l have rank \(0\).

Complex multiplication

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

Modular form 436810.2.a.l

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} - 2 q^{9} - q^{10} - q^{12} - 4 q^{13} - q^{14} - q^{15} + q^{16} + 2 q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 436810l

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436810.l1 436810l1 \([1, 1, 0, -26537117, 53458292221]\) \(-1693700041/32000\) \(-39047967719203791392000\) \([]\) \(43794432\) \(3.1295\) \(\Gamma_0(N)\)-optimal
436810.l2 436810l2 \([1, 1, 0, 105597908, 250048782416]\) \(106718863559/83886080\) \(-102361904497829586906644480\) \([]\) \(131383296\) \(3.6789\)