Properties

Label 6253.b
Number of curves 3
Conductor 6253
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("6253.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6253.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6253.b1 6253a3 [0, 1, 1, -316593, -68670260] [] 12960  
6253.b2 6253a2 [0, 1, 1, -3943, -93609] [] 4320  
6253.b3 6253a1 [0, 1, 1, -563, 4918] [] 1440 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6253.b have rank \(1\).

Modular form 6253.2.a.b

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

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.