Properties

Label 2800.g
Number of curves $6$
Conductor $2800$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2800.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.g1 2800v6 \([0, 1, 0, -1092208, 438981588]\) \(2251439055699625/25088\) \(1605632000000\) \([2]\) \(20736\) \(1.9110\)  
2800.g2 2800v5 \([0, 1, 0, -68208, 6853588]\) \(-548347731625/1835008\) \(-117440512000000\) \([2]\) \(10368\) \(1.5644\)  
2800.g3 2800v4 \([0, 1, 0, -14208, 529588]\) \(4956477625/941192\) \(60236288000000\) \([2]\) \(6912\) \(1.3617\)  
2800.g4 2800v2 \([0, 1, 0, -4208, -106412]\) \(128787625/98\) \(6272000000\) \([2]\) \(2304\) \(0.81236\)  
2800.g5 2800v1 \([0, 1, 0, -208, -2412]\) \(-15625/28\) \(-1792000000\) \([2]\) \(1152\) \(0.46578\) \(\Gamma_0(N)\)-optimal
2800.g6 2800v3 \([0, 1, 0, 1792, 49588]\) \(9938375/21952\) \(-1404928000000\) \([2]\) \(3456\) \(1.0151\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2800.2.a.g

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{7} + q^{9} + 4 q^{13} - 6 q^{17} - 2 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.