Properties

Label 133200.gt
Number of curves $4$
Conductor $133200$
CM no
Rank $0$
Graph

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

Elliptic curves in class 133200.gt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
133200.gt1 133200dr4 \([0, 0, 0, -1153650675, -3104981180750]\) \(3639478711331685826729/2016912141902025000\) \(94101052892580878400000000000\) \([2]\) \(106168320\) \(4.2500\)  
133200.gt2 133200dr2 \([0, 0, 0, -703650675, 7141968819250]\) \(825824067562227826729/5613755625000000\) \(261915382440000000000000000\) \([2, 2]\) \(53084160\) \(3.9034\)  
133200.gt3 133200dr1 \([0, 0, 0, -702498675, 7166652723250]\) \(821774646379511057449/38361600000\) \(1789798809600000000000\) \([2]\) \(26542080\) \(3.5568\) \(\Gamma_0(N)\)-optimal
133200.gt4 133200dr3 \([0, 0, 0, -272082675, 15809148963250]\) \(-47744008200656797609/2286529541015625000\) \(-106680322265625000000000000000\) \([2]\) \(106168320\) \(4.2500\)  

Rank

sage: E.rank()
 

The elliptic curves in class 133200.gt have rank \(0\).

Complex multiplication

The elliptic curves in class 133200.gt do not have complex multiplication.

Modular form 133200.2.a.gt

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.