Properties

Label 33800.n
Number of curves $2$
Conductor $33800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 33800.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33800.n1 33800m2 \([0, 0, 0, -39715, 2965950]\) \(5606442/169\) \(208827064576000\) \([2]\) \(107520\) \(1.5241\)  
33800.n2 33800m1 \([0, 0, 0, -5915, -109850]\) \(37044/13\) \(8031810176000\) \([2]\) \(53760\) \(1.1776\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 33800.n have rank \(0\).

Complex multiplication

The elliptic curves in class 33800.n do not have complex multiplication.

Modular form 33800.2.a.n

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} - 3 q^{9} + 2 q^{11} + 4 q^{17} + 2 q^{19} + O(q^{20})\) 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 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.