Properties

Label 48672.y
Number of curves $2$
Conductor $48672$
CM no
Rank $0$
Graph

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

Elliptic curves in class 48672.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48672.y1 48672m2 \([0, 0, 0, -1997580, 1086056192]\) \(61162984000/41067\) \(591889408135114752\) \([2]\) \(860160\) \(2.3486\)  
48672.y2 48672m1 \([0, 0, 0, -149565, 9772256]\) \(1643032000/767637\) \(172871545885616448\) \([2]\) \(430080\) \(2.0020\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 48672.y have rank \(0\).

Complex multiplication

The elliptic curves in class 48672.y do not have complex multiplication.

Modular form 48672.2.a.y

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} + 4 q^{11} + 6 q^{17} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.