Properties

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

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Show commands: SageMath
E = EllipticCurve("fj1")
 
E.isogeny_class()
 

Elliptic curves in class 100800fj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.oz4 100800fj1 \([0, 0, 0, -661575, -862373500]\) \(-43927191786304/415283203125\) \(-302741455078125000000\) \([2]\) \(2949120\) \(2.6123\) \(\Gamma_0(N)\)-optimal
100800.oz3 100800fj2 \([0, 0, 0, -18239700, -29901436000]\) \(14383655824793536/45209390625\) \(2109289329000000000000\) \([2, 2]\) \(5898240\) \(2.9589\)  
100800.oz2 100800fj3 \([0, 0, 0, -26114700, -1567186000]\) \(5276930158229192/3050936350875\) \(1138755891091392000000000\) \([2]\) \(11796480\) \(3.3055\)  
100800.oz1 100800fj4 \([0, 0, 0, -291614700, -1916735686000]\) \(7347751505995469192/72930375\) \(27221116608000000000\) \([2]\) \(11796480\) \(3.3055\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 100800.2.a.fj

sage: E.q_eigenform(10)
 
\(q + q^{7} + 4 q^{11} - 2 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.