Properties

Label 82800.g
Number of curves $4$
Conductor $82800$
CM no
Rank $0$
Graph

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

Elliptic curves in class 82800.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
82800.g1 82800bc4 \([0, 0, 0, -169275, 22684250]\) \(45989074372/7555707\) \(88129766448000000\) \([2]\) \(786432\) \(1.9731\)  
82800.g2 82800bc2 \([0, 0, 0, -47775, -3681250]\) \(4135597648/385641\) \(1124529156000000\) \([2, 2]\) \(393216\) \(1.6265\)  
82800.g3 82800bc1 \([0, 0, 0, -46650, -3878125]\) \(61604313088/621\) \(113177250000\) \([2]\) \(196608\) \(1.2799\) \(\Gamma_0(N)\)-optimal
82800.g4 82800bc3 \([0, 0, 0, 55725, -17446750]\) \(1640689628/12223143\) \(-142570739952000000\) \([2]\) \(786432\) \(1.9731\)  

Rank

sage: E.rank()
 

The elliptic curves in class 82800.g have rank \(0\).

Complex multiplication

The elliptic curves in class 82800.g do not have complex multiplication.

Modular form 82800.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.