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Properties

Label 11550.t
Number of curves $2$
Conductor $11550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 11550.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11550.t1 11550t1 \([1, 0, 1, -124876, -16994602]\) \(13782741913468081/701662500\) \(10963476562500\) \([2]\) \(69120\) \(1.5721\) \(\Gamma_0(N)\)-optimal
11550.t2 11550t2 \([1, 0, 1, -118126, -18911602]\) \(-11666347147400401/3126621093750\) \(-48853454589843750\) \([2]\) \(138240\) \(1.9187\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11550.t have rank \(0\).

Complex multiplication

The elliptic curves in class 11550.t do not have complex multiplication.

Modular form 11550.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - q^{11} + q^{12} - 4 q^{13} + q^{14} + q^{16} + 4 q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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 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.