Properties

Label 705600.et
Number of curves $4$
Conductor $705600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 705600.et

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.et1 \([0, 0, 0, -49406700, -133667786000]\) \(303735479048/105\) \(4610786664960000000\) \([2]\) \(56623104\) \(2.9371\)
705600.et2 \([0, 0, 0, -3101700, -2068976000]\) \(601211584/11025\) \(60516574977600000000\) \([2, 2]\) \(28311552\) \(2.5906\)
705600.et3 \([0, 0, 0, -400575, 48706000]\) \(82881856/36015\) \(3088866847815000000\) \([2]\) \(14155776\) \(2.2440\)
705600.et4 \([0, 0, 0, -14700, -6001814000]\) \(-8/354375\) \(-15561404994240000000000\) \([2]\) \(56623104\) \(2.9371\)

Rank

sage: E.rank()
 

The elliptic curves in class 705600.et have rank \(0\).

Complex multiplication

The elliptic curves in class 705600.et do not have complex multiplication.

Modular form 705600.2.a.et

sage: E.q_eigenform(10)
 
\(q - 4q^{11} - 6q^{13} + 6q^{17} - 4q^{19} + O(q^{20})\)  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 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.