Properties

Label 187200.fk
Number of curves $2$
Conductor $187200$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("fk1")
 
E.isogeny_class()
 

Elliptic curves in class 187200.fk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.fk1 187200dn2 \([0, 0, 0, -1188300, -498418000]\) \(497169541448/190125\) \(70963776000000000\) \([2]\) \(2949120\) \(2.1993\)  
187200.fk2 187200dn1 \([0, 0, 0, -63300, -10168000]\) \(-601211584/609375\) \(-28431000000000000\) \([2]\) \(1474560\) \(1.8528\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 187200.fk have rank \(0\).

Complex multiplication

The elliptic curves in class 187200.fk do not have complex multiplication.

Modular form 187200.2.a.fk

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} + 4 q^{11} + q^{13} + 6 q^{19} + O(q^{20})\) 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 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.