Properties

Label 277200.gt
Number of curves $2$
Conductor $277200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 277200.gt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277200.gt1 277200gt2 \([0, 0, 0, -116175, 15214250]\) \(59466754384/121275\) \(353637900000000\) \([2]\) \(1474560\) \(1.6781\)  
277200.gt2 277200gt1 \([0, 0, 0, -4800, 401375]\) \(-67108864/343035\) \(-62518128750000\) \([2]\) \(737280\) \(1.3315\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 277200.gt have rank \(0\).

Complex multiplication

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

Modular form 277200.2.a.gt

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