Properties

Label 3120.y
Number of curves $2$
Conductor $3120$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3120.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3120.y1 3120x2 \([0, 1, 0, -13640, 608628]\) \(68523370149961/243360\) \(996802560\) \([2]\) \(3840\) \(0.94498\)  
3120.y2 3120x1 \([0, 1, 0, -840, 9588]\) \(-16022066761/998400\) \(-4089446400\) \([2]\) \(1920\) \(0.59841\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3120.y have rank \(0\).

Complex multiplication

The elliptic curves in class 3120.y do not have complex multiplication.

Modular form 3120.2.a.y

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + 2 q^{7} + q^{9} - 4 q^{11} - q^{13} + q^{15} + 4 q^{17} + 2 q^{19} + O(q^{20})\)  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.