Properties

Label 100800mg
Number of curves $4$
Conductor $100800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("mg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800mg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.p4 100800mg1 \([0, 0, 0, 33300, -3726000]\) \(1367631/2800\) \(-8360755200000000\) \([2]\) \(589824\) \(1.7396\) \(\Gamma_0(N)\)-optimal
100800.p3 100800mg2 \([0, 0, 0, -254700, -40014000]\) \(611960049/122500\) \(365783040000000000\) \([2, 2]\) \(1179648\) \(2.0862\)  
100800.p2 100800mg3 \([0, 0, 0, -1262700, 510354000]\) \(74565301329/5468750\) \(16329600000000000000\) \([2]\) \(2359296\) \(2.4327\)  
100800.p1 100800mg4 \([0, 0, 0, -3854700, -2912814000]\) \(2121328796049/120050\) \(358467379200000000\) \([2]\) \(2359296\) \(2.4327\)  

Rank

sage: E.rank()
 

The elliptic curves in class 100800mg have rank \(1\).

Complex multiplication

The elliptic curves in class 100800mg do not have complex multiplication.

Modular form 100800.2.a.mg

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