Properties

Label 6300.p
Number of curves 4
Conductor 6300
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6300.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6300.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6300.p1 6300j4 [0, 0, 0, -411375, 101555750] [2] 41472  
6300.p2 6300j3 [0, 0, 0, -25500, 1614125] [2] 20736  
6300.p3 6300j2 [0, 0, 0, -6375, 62750] [2] 13824  
6300.p4 6300j1 [0, 0, 0, 1500, 7625] [2] 6912 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6300.p have rank \(1\).

Modular form 6300.2.a.p

sage: E.q_eigenform(10)
 
\( q - q^{7} + 6q^{11} - 2q^{13} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.