Properties

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

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Show commands: SageMath
E = EllipticCurve("ox1")
 
E.isogeny_class()
 

Elliptic curves in class 176400.ox

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.ox1 176400km2 \([0, 0, 0, -717675, -234011750]\) \(68971442301/400\) \(237081600000000\) \([2]\) \(1179648\) \(1.9485\)  
176400.ox2 176400km1 \([0, 0, 0, -45675, -3515750]\) \(17779581/1280\) \(758661120000000\) \([2]\) \(589824\) \(1.6019\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 176400.2.a.ox

sage: E.q_eigenform(10)
 
\(q + 2 q^{11} + 2 q^{13} - 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.