Properties

Label 6600.u
Number of curves $2$
Conductor $6600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 6600.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6600.u1 6600ba1 \([0, 1, 0, -283, -562]\) \(10061824/5445\) \(1361250000\) \([2]\) \(3072\) \(0.44363\) \(\Gamma_0(N)\)-optimal
6600.u2 6600ba2 \([0, 1, 0, 1092, -3312]\) \(35969456/22275\) \(-89100000000\) \([2]\) \(6144\) \(0.79021\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6600.u have rank \(1\).

Complex multiplication

The elliptic curves in class 6600.u do not have complex multiplication.

Modular form 6600.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{7} + q^{9} - q^{11} + 4 q^{13} - 4 q^{19} + O(q^{20})\) 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.