Properties

Label 176400qp
Number of curves $2$
Conductor $176400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("qp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176400qp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.sj2 176400qp1 \([0, 0, 0, 437325, -121850750]\) \(19652/25\) \(-11767111801200000000\) \([2]\) \(3096576\) \(2.3453\) \(\Gamma_0(N)\)-optimal
176400.sj1 176400qp2 \([0, 0, 0, -2649675, -1180691750]\) \(2185454/625\) \(588355590060000000000\) \([2]\) \(6193152\) \(2.6919\)  

Rank

sage: E.rank()
 

The elliptic curves in class 176400qp have rank \(1\).

Complex multiplication

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

Modular form 176400.2.a.qp

sage: E.q_eigenform(10)
 
\(q + 4 q^{11} + 2 q^{13} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.