Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("byh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 705600.byh

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.byh1 \([0, 0, 0, -4500846014700, -3675270815038186000]\) \(229625675762164624948320008/9568125\) \(420157934844480000000000\) \([2]\) \(7927234560\) \(5.4335\)
705600.byh2 \([0, 0, 0, -281302889700, -57426100576936000]\) \(448487713888272974160064/91549016015625\) \(502515455041730025000000000000\) \([2, 2]\) \(3963617280\) \(5.0870\)
705600.byh3 \([0, 0, 0, -280338422700, -57839426767654000]\) \(-55486311952875723077768/801237030029296875\) \(-35184123938392734375000000000000000\) \([2]\) \(7927234560\) \(5.4335\)
705600.byh4 \([0, 0, 0, -17641723575, -890818691749000]\) \(7079962908642659949376/100085966990454375\) \(8583985155305315771229375000000\) \([2]\) \(1981808640\) \(4.7404\)

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 705600.2.a.byh

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.