Properties

Label 91200hk
Number of curves $4$
Conductor $91200$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("hk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 91200hk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91200.hi3 91200hk1 \([0, 1, 0, -49633, -4247137]\) \(3301293169/22800\) \(93388800000000\) \([2]\) \(294912\) \(1.5142\) \(\Gamma_0(N)\)-optimal
91200.hi2 91200hk2 \([0, 1, 0, -81633, 1864863]\) \(14688124849/8122500\) \(33269760000000000\) \([2, 2]\) \(589824\) \(1.8608\)  
91200.hi4 91200hk3 \([0, 1, 0, 318367, 15064863]\) \(871257511151/527800050\) \(-2161869004800000000\) \([2]\) \(1179648\) \(2.2074\)  
91200.hi1 91200hk4 \([0, 1, 0, -993633, 380344863]\) \(26487576322129/44531250\) \(182400000000000000\) \([2]\) \(1179648\) \(2.2074\)  

Rank

sage: E.rank()
 

The elliptic curves in class 91200hk have rank \(1\).

Complex multiplication

The elliptic curves in class 91200hk do not have complex multiplication.

Modular form 91200.2.a.hk

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} + 4q^{11} + 2q^{13} - 2q^{17} - q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.