Properties

Label 106470ce
Number of curves $8$
Conductor $106470$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 106470ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106470.cg7 106470ce1 \([1, -1, 0, -756729, -253085715]\) \(13619385906841/6048000\) \(21281362266528000\) \([2]\) \(1769472\) \(2.0916\) \(\Gamma_0(N)\)-optimal
106470.cg6 106470ce2 \([1, -1, 0, -878409, -166133187]\) \(21302308926361/8930250000\) \(31423261471670250000\) \([2, 2]\) \(3538944\) \(2.4382\)  
106470.cg5 106470ce3 \([1, -1, 0, -2239704, 981046080]\) \(353108405631241/86318776320\) \(303733655633154539520\) \([2]\) \(5308416\) \(2.6409\)  
106470.cg8 106470ce4 \([1, -1, 0, 2924091, -1222467687]\) \(785793873833639/637994920500\) \(-2244940646059066000500\) \([2]\) \(7077888\) \(2.7847\)  
106470.cg4 106470ce5 \([1, -1, 0, -6627789, 6453702945]\) \(9150443179640281/184570312500\) \(649455635575195312500\) \([2]\) \(7077888\) \(2.7847\)  
106470.cg2 106470ce6 \([1, -1, 0, -33389784, 74264724288]\) \(1169975873419524361/108425318400\) \(381520912654438502400\) \([2, 2]\) \(10616832\) \(2.9875\)  
106470.cg3 106470ce7 \([1, -1, 0, -30956184, 85547380608]\) \(-932348627918877961/358766164249920\) \(-1262406202112307244749120\) \([2]\) \(21233664\) \(3.3340\)  
106470.cg1 106470ce8 \([1, -1, 0, -534224664, 4752763672320]\) \(4791901410190533590281/41160000\) \(144831493202760000\) \([2]\) \(21233664\) \(3.3340\)  

Rank

sage: E.rank()
 

The elliptic curves in class 106470ce have rank \(1\).

Complex multiplication

The elliptic curves in class 106470ce do not have complex multiplication.

Modular form 106470.2.a.ce

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + q^{14} + q^{16} + 6 q^{17} - 8 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.