Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 85176.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.cd1 85176bj1 \([0, 0, 0, -14703, -681070]\) \(10536048/91\) \(3036024246528\) \([2]\) \(301056\) \(1.2195\) \(\Gamma_0(N)\)-optimal
85176.cd2 85176bj2 \([0, 0, 0, -4563, -1603810]\) \(-78732/8281\) \(-1105112825736192\) \([2]\) \(602112\) \(1.5661\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 85176.2.a.cd

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