Properties

Label 163800.dl
Number of curves $2$
Conductor $163800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dl1")
 
E.isogeny_class()
 

Elliptic curves in class 163800.dl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163800.dl1 163800y1 \([0, 0, 0, -3042675, -2042813250]\) \(267080942160036/1990625\) \(23218650000000000\) \([2]\) \(3440640\) \(2.3163\) \(\Gamma_0(N)\)-optimal
163800.dl2 163800y2 \([0, 0, 0, -2979675, -2131454250]\) \(-125415986034978/11552734375\) \(-269502187500000000000\) \([2]\) \(6881280\) \(2.6628\)  

Rank

sage: E.rank()
 

The elliptic curves in class 163800.dl have rank \(0\).

Complex multiplication

The elliptic curves in class 163800.dl do not have complex multiplication.

Modular form 163800.2.a.dl

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