Properties

Label 46800.eo
Number of curves $2$
Conductor $46800$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("eo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800.eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.eo1 46800dz2 \([0, 0, 0, -165675, -23251750]\) \(10779215329/1232010\) \(57480658560000000\) \([2]\) \(442368\) \(1.9481\)  
46800.eo2 46800dz1 \([0, 0, 0, 14325, -1831750]\) \(6967871/35100\) \(-1637625600000000\) \([2]\) \(221184\) \(1.6016\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 46800.eo have rank \(0\).

Complex multiplication

The elliptic curves in class 46800.eo do not have complex multiplication.

Modular form 46800.2.a.eo

sage: E.q_eigenform(10)
 
\(q + 2q^{7} + 4q^{11} + q^{13} + 8q^{17} + 6q^{19} + O(q^{20})\)  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.