Properties

Label 6450.bc
Number of curves $2$
Conductor $6450$
CM no
Rank $1$
Graph

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

Elliptic curves in class 6450.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6450.bc1 6450bb2 \([1, 1, 1, -5938, -172969]\) \(1481933914201/53916840\) \(842450625000\) \([2]\) \(13824\) \(1.0580\)  
6450.bc2 6450bb1 \([1, 1, 1, -938, 7031]\) \(5841725401/1857600\) \(29025000000\) \([2]\) \(6912\) \(0.71145\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6450.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 6450.bc do not have complex multiplication.

Modular form 6450.2.a.bc

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