Properties

Label 277200iq
Number of curves $4$
Conductor $277200$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("iq1")
 
E.isogeny_class()
 

Elliptic curves in class 277200iq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277200.iq2 277200iq1 \([0, 0, 0, -166200, -26079125]\) \(75216478666752/326095\) \(2201141250000\) \([2]\) \(995328\) \(1.5752\) \(\Gamma_0(N)\)-optimal
277200.iq3 277200iq2 \([0, 0, 0, -163575, -26942750]\) \(-4481782160112/310023175\) \(-33482502900000000\) \([2]\) \(1990656\) \(1.9217\)  
277200.iq1 277200iq3 \([0, 0, 0, -232200, -3479625]\) \(281370820608/161767375\) \(796016810531250000\) \([2]\) \(2985984\) \(2.1245\)  
277200.iq4 277200iq4 \([0, 0, 0, 925425, -27789750]\) \(1113258734352/648484375\) \(-51056471812500000000\) \([2]\) \(5971968\) \(2.4711\)  

Rank

sage: E.rank()
 

The elliptic curves in class 277200iq have rank \(1\).

Complex multiplication

The elliptic curves in class 277200iq do not have complex multiplication.

Modular form 277200.2.a.iq

sage: E.q_eigenform(10)
 
\(q + q^{7} - q^{11} - 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.