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Properties

Label 11970.x
Number of curves $2$
Conductor $11970$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 11970.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11970.x1 11970k2 \([1, -1, 0, -35164869, -80253512875]\) \(-244320235433784441003267/10427200000\) \(-205238577600000\) \([]\) \(699840\) \(2.6792\)  
11970.x2 11970k1 \([1, -1, 0, -430494, -111928500]\) \(-326784782222946131643/11721923828125000\) \(-316491943359375000\) \([3]\) \(233280\) \(2.1299\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11970.x have rank \(0\).

Complex multiplication

The elliptic curves in class 11970.x do not have complex multiplication.

Modular form 11970.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} - 3 q^{11} - 7 q^{13} - q^{14} + q^{16} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.