Properties

Label 176400fk
Number of curves $2$
Conductor $176400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fk1")
 
E.isogeny_class()
 

Elliptic curves in class 176400fk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.lk2 176400fk1 \([0, 0, 0, -1155, -12670]\) \(46585/8\) \(29262643200\) \([]\) \(124416\) \(0.72867\) \(\Gamma_0(N)\)-optimal
176400.lk1 176400fk2 \([0, 0, 0, -26355, 1645490]\) \(553463785/512\) \(1872809164800\) \([]\) \(373248\) \(1.2780\)  

Rank

sage: E.rank()
 

The elliptic curves in class 176400fk have rank \(0\).

Complex multiplication

The elliptic curves in class 176400fk do not have complex multiplication.

Modular form 176400.2.a.fk

sage: E.q_eigenform(10)
 
\(q + 2 q^{13} + 3 q^{17} + 8 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.