Properties

Label 221760ma
Number of curves $4$
Conductor $221760$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ma1")
 
E.isogeny_class()
 

Elliptic curves in class 221760ma

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221760.s3 221760ma1 \([0, 0, 0, -1494408, 703156232]\) \(494428821070157824/77818125\) \(58090919040000\) \([2]\) \(1966080\) \(2.0448\) \(\Gamma_0(N)\)-optimal
221760.s2 221760ma2 \([0, 0, 0, -1498908, 698708432]\) \(31181799673942864/387562277025\) \(4629019032800870400\) \([2, 2]\) \(3932160\) \(2.3914\)  
221760.s4 221760ma3 \([0, 0, 0, -264108, 1815461552]\) \(-42644293386916/29777663954115\) \(-1422650049989825986560\) \([2]\) \(7864320\) \(2.7380\)  
221760.s1 221760ma4 \([0, 0, 0, -2805708, -702703888]\) \(51126217658776516/25121936269815\) \(1200219196010996367360\) \([2]\) \(7864320\) \(2.7380\)  

Rank

sage: E.rank()
 

The elliptic curves in class 221760ma have rank \(0\).

Complex multiplication

The elliptic curves in class 221760ma do not have complex multiplication.

Modular form 221760.2.a.ma

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - q^{11} - 2 q^{13} + 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.