Properties

Label 254320h
Number of curves $2$
Conductor $254320$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 254320h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254320.h1 254320h1 \([0, 1, 0, -75525, -8505377]\) \(-7710244864/565675\) \(-3495428952083200\) \([]\) \(1824768\) \(1.7317\) \(\Gamma_0(N)\)-optimal
254320.h2 254320h2 \([0, 1, 0, 433115, -6318225]\) \(1454115454976/844421875\) \(-5217866565868000000\) \([]\) \(5474304\) \(2.2810\)  

Rank

sage: E.rank()
 

The elliptic curves in class 254320h have rank \(2\).

Complex multiplication

The elliptic curves in class 254320h do not have complex multiplication.

Modular form 254320.2.a.h

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{5} - q^{7} + q^{9} + q^{11} - 4 q^{13} - 2 q^{15} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.