Properties

Label 85176.r
Number of curves $2$
Conductor $85176$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 85176.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.r1 85176i2 \([0, 0, 0, -168831, -26693550]\) \(21882096/7\) \(170250898132224\) \([2]\) \(442368\) \(1.7055\)  
85176.r2 85176i1 \([0, 0, 0, -9126, -533871]\) \(-55296/49\) \(-74484767932848\) \([2]\) \(221184\) \(1.3589\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 85176.2.a.r

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + q^{7} - 2 q^{11} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.