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Properties

Label 6050.bc
Number of curves $2$
Conductor $6050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 6050.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6050.bc1 6050bc1 \([1, 1, 1, -3088, -181719]\) \(-117649/440\) \(-12179481875000\) \([]\) \(11520\) \(1.1966\) \(\Gamma_0(N)\)-optimal
6050.bc2 6050bc2 \([1, 1, 1, 27162, 4295281]\) \(80062991/332750\) \(-9210733167968750\) \([]\) \(34560\) \(1.7459\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6050.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 6050.bc do not have complex multiplication.

Modular form 6050.2.a.bc

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.