↑

Properties

Label 308550fh
Number of curves $2$
Conductor $308550$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("fh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 308550fh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
308550.fh1 308550fh1 [1, 1, 1, -2734663, -1728001219] [2] 17203200 \(\Gamma_0(N)\)-optimal
308550.fh2 308550fh2 [1, 1, 1, -798663, -4124769219] [2] 34406400  

Rank

sage: E.rank()
 

The elliptic curves in class 308550fh have rank \(1\).

Complex multiplication

The elliptic curves in class 308550fh do not have complex multiplication.

Modular form 308550.2.a.fh

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{6} - 4q^{7} + q^{8} + q^{9} - q^{12} - 4q^{13} - 4q^{14} + q^{16} - q^{17} + q^{18} + 8q^{19} + O(q^{20}) \)

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.