Properties

Label 224400.fl
Number of curves $2$
Conductor $224400$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("fl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 224400.fl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
224400.fl1 224400bt1 \([0, 1, 0, -78408, 8419188]\) \(832972004929/610368\) \(39063552000000\) \([2]\) \(737280\) \(1.5422\) \(\Gamma_0(N)\)-optimal
224400.fl2 224400bt2 \([0, 1, 0, -62408, 11971188]\) \(-420021471169/727634952\) \(-46568636928000000\) \([2]\) \(1474560\) \(1.8888\)  

Rank

sage: E.rank()
 

The elliptic curves in class 224400.fl have rank \(2\).

Complex multiplication

The elliptic curves in class 224400.fl do not have complex multiplication.

Modular form 224400.2.a.fl

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{7} + q^{9} - q^{11} + q^{17} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.