Properties

Label 85176.y
Number of curves $2$
Conductor $85176$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 85176.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.y1 85176m2 \([0, 0, 0, -253076655, -1549622431838]\) \(1989996724085074000/1843096437\) \(1660258326685460366592\) \([2]\) \(10321920\) \(3.3687\)  
85176.y2 85176m1 \([0, 0, 0, -15701790, -24583874159]\) \(-7604375980288000/236743082667\) \(-13328611921510615849392\) \([2]\) \(5160960\) \(3.0221\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 85176.y have rank \(0\).

Complex multiplication

The elliptic curves in class 85176.y do not have complex multiplication.

Modular form 85176.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{7} - 2 q^{11} + 6 q^{17} + 8 q^{19} + O(q^{20})\) 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.