↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve([0, 0, 0, -3704414700, -86781571814000]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

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

Complex multiplication

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

Modular form 705600.2.a.bxc

Copy content sage:E.q_eigenform(10)
 
\(q + 4 q^{11} + 2 q^{13} + 2 q^{17} + 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 705600.bxc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.bxc1 \([0, 0, 0, -3704414700, -86781571814000]\) \(128025588102048008/7875\) \(345808999872000000000\) \([2]\) \(226492416\) \(3.8495\)
705600.bxc2 \([0, 0, 0, -259322700, -1010005346000]\) \(43919722445768/15380859375\) \(675408202875000000000000000\) \([2]\) \(226492416\) \(3.8495\)
705600.bxc3 \([0, 0, 0, -231539700, -1355792564000]\) \(250094631024064/62015625\) \(340405734249000000000000\) \([2, 2]\) \(113246208\) \(3.5029\)
705600.bxc4 \([0, 0, 0, -12748575, -26417688500]\) \(-2671731885376/1969120125\) \(-168883794904285125000000\) \([2]\) \(56623104\) \(3.1564\)