Properties

Label 930.j
Number of curves $2$
Conductor $930$
CM no
Rank $0$
Graph

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

Elliptic curves in class 930.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.j1 930j2 \([1, 0, 1, -218448, 39279646]\) \(1152829477932246539641/3188367360\) \(3188367360\) \([2]\) \(4160\) \(1.4817\)  
930.j2 930j1 \([1, 0, 1, -13648, 613406]\) \(-281115640967896441/468084326400\) \(-468084326400\) \([2]\) \(2080\) \(1.1351\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 930.j have rank \(0\).

Complex multiplication

The elliptic curves in class 930.j do not have complex multiplication.

Modular form 930.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 4q^{7} - q^{8} + q^{9} - q^{10} + 2q^{11} + q^{12} + 2q^{13} - 4q^{14} + q^{15} + q^{16} - q^{18} + O(q^{20})\)  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.