Properties

Label 14400fh
Number of curves $2$
Conductor $14400$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 14400fh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.p2 14400fh1 \([0, 0, 0, -28875, 2225000]\) \(-29218112/6561\) \(-597871125000000\) \([2]\) \(61440\) \(1.5555\) \(\Gamma_0(N)\)-optimal
14400.p1 14400fh2 \([0, 0, 0, -484500, 129800000]\) \(2156689088/81\) \(472392000000000\) \([2]\) \(122880\) \(1.9021\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14400fh have rank \(0\).

Complex multiplication

The elliptic curves in class 14400fh do not have complex multiplication.

Modular form 14400.2.a.fh

sage: E.q_eigenform(10)
 
\(q - 4q^{7} + 4q^{13} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.