Properties

Label 6450.t
Number of curves $4$
Conductor $6450$
CM no
Rank $1$
Graph

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

Elliptic curves in class 6450.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6450.t1 6450bd3 [1, 1, 1, -20963, 1151531] [2] 18432  
6450.t2 6450bd2 [1, 1, 1, -2213, -10969] [2, 2] 9216  
6450.t3 6450bd1 [1, 1, 1, -1713, -27969] [2] 4608 \(\Gamma_0(N)\)-optimal
6450.t4 6450bd4 [1, 1, 1, 8537, -75469] [2] 18432  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6450.2.a.t

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.