Properties

Label 2800.m
Number of curves $4$
Conductor $2800$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2800.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.m1 2800o4 \([0, 0, 0, -107075, 13485250]\) \(2121328796049/120050\) \(7683200000000\) \([2]\) \(9216\) \(1.5369\)  
2800.m2 2800o3 \([0, 0, 0, -35075, -2362750]\) \(74565301329/5468750\) \(350000000000000\) \([2]\) \(9216\) \(1.5369\)  
2800.m3 2800o2 \([0, 0, 0, -7075, 185250]\) \(611960049/122500\) \(7840000000000\) \([2, 2]\) \(4608\) \(1.1903\)  
2800.m4 2800o1 \([0, 0, 0, 925, 17250]\) \(1367631/2800\) \(-179200000000\) \([2]\) \(2304\) \(0.84371\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2800.m have rank \(0\).

Complex multiplication

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

Modular form 2800.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{7} - 3q^{9} - 4q^{11} + 6q^{13} - 2q^{17} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.