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Properties

Label 167310d
Number of curves $2$
Conductor $167310$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 167310d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
167310.er2 167310d1 \([1, -1, 1, 15178, 2901669]\) \(109902239/1100000\) \(-3870618137100000\) \([]\) \(1152000\) \(1.6721\) \(\Gamma_0(N)\)-optimal
167310.er1 167310d2 \([1, -1, 1, -9034772, 10454848629]\) \(-23178622194826561/1610510\) \(-5666972014528110\) \([]\) \(5760000\) \(2.4769\)  

Rank

sage: E.rank()
 

The elliptic curves in class 167310d have rank \(1\).

Complex multiplication

The elliptic curves in class 167310d do not have complex multiplication.

Modular form 167310.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - 3 q^{7} + q^{8} + q^{10} + q^{11} - 3 q^{14} + q^{16} + 7 q^{17} - 5 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.