Properties

Label 705600.zu
Number of curves $4$
Conductor $705600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("zu1")
 
E.isogeny_class()
 

Elliptic curves in class 705600.zu

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.zu1 \([0, 0, 0, -622706700, 5980987726000]\) \(608119035935048/826875\) \(36309944986560000000000\) \([2]\) \(113246208\) \(3.6031\)
705600.zu2 \([0, 0, 0, -98798700, -252517286000]\) \(2428799546888/778248135\) \(34174629741790379520000000\) \([2]\) \(113246208\) \(3.6031\)
705600.zu3 \([0, 0, 0, -39263700, 91714084000]\) \(1219555693504/43758225\) \(240190286086094400000000\) \([2, 2]\) \(56623104\) \(3.2565\)
705600.zu4 \([0, 0, 0, 922425, 5072798500]\) \(1012048064/130203045\) \(-11167010112038445000000\) \([2]\) \(28311552\) \(2.9100\)

Rank

sage: E.rank()
 

The elliptic curves in class 705600.zu have rank \(1\).

Complex multiplication

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

Modular form 705600.2.a.zu

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