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Properties

Label 6270.j
Number of curves $4$
Conductor $6270$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 6270.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6270.j1 6270j3 \([1, 0, 1, -122614, -16535758]\) \(203863183638431173849/1862190\) \(1862190\) \([2]\) \(21504\) \(1.2401\)  
6270.j2 6270j4 \([1, 0, 1, -8234, -218254]\) \(61727754446114329/15273070271250\) \(15273070271250\) \([2]\) \(21504\) \(1.2401\)  
6270.j3 6270j2 \([1, 0, 1, -7664, -258838]\) \(49774710096861049/4756860900\) \(4756860900\) \([2, 2]\) \(10752\) \(0.89354\)  
6270.j4 6270j1 \([1, 0, 1, -444, -4694]\) \(-9648632960569/3784521840\) \(-3784521840\) \([2]\) \(5376\) \(0.54697\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6270.j have rank \(0\).

Complex multiplication

The elliptic curves in class 6270.j do not have complex multiplication.

Modular form 6270.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + q^{11} + q^{12} + 6 q^{13} - q^{15} + q^{16} + 6 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.