Properties

Label 88200gt
Number of curves $4$
Conductor $88200$
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 88200gt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
88200.hm4 88200gt1 [0, 0, 0, 11025, 2315250] [2] 393216 \(\Gamma_0(N)\)-optimal
88200.hm3 88200gt2 [0, 0, 0, -209475, 34728750] [2, 2] 786432  
88200.hm2 88200gt3 [0, 0, 0, -650475, -159752250] [2] 1572864  
88200.hm1 88200gt4 [0, 0, 0, -3296475, 2303673750] [2] 1572864  

Rank

sage: E.rank()
 

The elliptic curves in class 88200gt have rank \(0\).

Complex multiplication

The elliptic curves in class 88200gt do not have complex multiplication.

Modular form 88200.2.a.gt

sage: E.q_eigenform(10)
 
\( q + 4q^{11} + 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20}) \)

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.