Properties

Label 2800.z
Number of curves $3$
Conductor $2800$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2800.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.z1 2800s3 \([0, 1, 0, -52533, 4830563]\) \(-250523582464/13671875\) \(-875000000000000\) \([]\) \(10368\) \(1.6253\)  
2800.z2 2800s1 \([0, 1, 0, -533, -5437]\) \(-262144/35\) \(-2240000000\) \([]\) \(1152\) \(0.52672\) \(\Gamma_0(N)\)-optimal
2800.z3 2800s2 \([0, 1, 0, 3467, 14563]\) \(71991296/42875\) \(-2744000000000\) \([]\) \(3456\) \(1.0760\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2800.z have rank \(1\).

Complex multiplication

The elliptic curves in class 2800.z do not have complex multiplication.

Modular form 2800.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} - 2q^{9} + 3q^{11} - 5q^{13} - 3q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.