Properties

Label 11600t
Number of curves $2$
Conductor $11600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 11600t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11600.g2 11600t1 \([0, -1, 0, 1992, -57488]\) \(13651919/29696\) \(-1900544000000\) \([]\) \(13440\) \(1.0403\) \(\Gamma_0(N)\)-optimal
11600.g1 11600t2 \([0, -1, 0, -182008, 30150512]\) \(-10418796526321/82044596\) \(-5250854144000000\) \([]\) \(67200\) \(1.8450\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11600t have rank \(0\).

Complex multiplication

The elliptic curves in class 11600t do not have complex multiplication.

Modular form 11600.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{7} - 2 q^{9} + 3 q^{11} + q^{13} - 8 q^{17} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.