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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bv1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

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

Complex multiplication

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

Modular form 705600.2.a.bv

Copy content sage:E.q_eigenform(10)
 
\(q - 6 q^{11} + 4 q^{13} - 6 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 705600.bv

Copy content sage:E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.bv1 \([0, 0, 0, -13288800, 17221687000]\) \(189123395584/16078125\) \(22063334627250000000000\) \([2]\) \(63700992\) \(3.0288\)
705600.bv2 \([0, 0, 0, -2704800, -1707797000]\) \(1594753024/4725\) \(6483918747600000000\) \([2]\) \(21233664\) \(2.4795\)
705600.bv3 \([0, 0, 0, -1602300, -3112382000]\) \(-20720464/178605\) \(-3921474058548480000000\) \([2]\) \(42467328\) \(2.8260\)
705600.bv4 \([0, 0, 0, 14273700, 79347562000]\) \(14647977776/132355125\) \(-2906005930424352000000000\) \([2]\) \(127401984\) \(3.3753\)