Properties

Label 104400et
Number of curves $2$
Conductor $104400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("et1")
 
E.isogeny_class()
 

Elliptic curves in class 104400et

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
104400.bp2 104400et1 \([0, 0, 0, 17925, 1534250]\) \(13651919/29696\) \(-1385496576000000\) \([]\) \(403200\) \(1.5896\) \(\Gamma_0(N)\)-optimal
104400.bp1 104400et2 \([0, 0, 0, -1638075, -812425750]\) \(-10418796526321/82044596\) \(-3827872670976000000\) \([]\) \(2016000\) \(2.3943\)  

Rank

sage: E.rank()
 

The elliptic curves in class 104400et have rank \(0\).

Complex multiplication

The elliptic curves in class 104400et do not have complex multiplication.

Modular form 104400.2.a.et

sage: E.q_eigenform(10)
 
\(q - 2 q^{7} - 3 q^{11} + q^{13} + 8 q^{17} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.