Properties

Label 202800.p
Number of curves $2$
Conductor $202800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 202800.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
202800.p1 202800jd2 \([0, -1, 0, -288484408, 1884514711312]\) \(7824392006186/7381125\) \(2504740333905108000000000\) \([2]\) \(71884800\) \(3.6039\)  
202800.p2 202800jd1 \([0, -1, 0, -13859408, 43428711312]\) \(-1735192372/3796875\) \(-644223336909750000000000\) \([2]\) \(35942400\) \(3.2573\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 202800.p have rank \(0\).

Complex multiplication

The elliptic curves in class 202800.p do not have complex multiplication.

Modular form 202800.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} + 4 q^{11} + 8 q^{17} + O(q^{20})\) 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.