Properties

Label 100800.ma
Number of curves $4$
Conductor $100800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ma1")
 
E.isogeny_class()
 

Elliptic curves in class 100800.ma

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.ma1 100800my4 \([0, 0, 0, -3362700, -2373446000]\) \(5633270409316/14175\) \(10581580800000000\) \([2]\) \(1572864\) \(2.3131\)  
100800.ma2 100800my3 \([0, 0, 0, -590700, 127906000]\) \(30534944836/8203125\) \(6123600000000000000\) \([2]\) \(1572864\) \(2.3131\)  
100800.ma3 100800my2 \([0, 0, 0, -212700, -36146000]\) \(5702413264/275625\) \(51438240000000000\) \([2, 2]\) \(786432\) \(1.9665\)  
100800.ma4 100800my1 \([0, 0, 0, 7800, -2189000]\) \(4499456/180075\) \(-2100394800000000\) \([2]\) \(393216\) \(1.6199\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 100800.ma have rank \(0\).

Complex multiplication

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

Modular form 100800.2.a.ma

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.