Properties

Label 364650.b
Number of curves $4$
Conductor $364650$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 364650.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.b1 364650b4 \([1, 1, 0, -290425831625, -60242342153812875]\) \(173384156893208913680898166749513361/466915159846072080\) \(7295549372594876250000\) \([2]\) \(1528823808\) \(4.7974\)  
364650.b2 364650b2 \([1, 1, 0, -18151621625, -941291490022875]\) \(42330166443562126960455979919761/69464630166853628678400\) \(1085384846357087948100000000\) \([2, 2]\) \(764411904\) \(4.4508\)  
364650.b3 364650b3 \([1, 1, 0, -17975203625, -960484533496875]\) \(-41107885916860358643135963073681/1716440731291073126286090000\) \(-26819386426423017598220156250000\) \([2]\) \(1528823808\) \(4.7974\)  
364650.b4 364650b1 \([1, 1, 0, -1145509625, -14407367686875]\) \(10638978093366640576603658641/418238874164098875064320\) \(6534982408814044922880000000\) \([2]\) \(382205952\) \(4.1043\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 364650.b have rank \(1\).

Complex multiplication

The elliptic curves in class 364650.b do not have complex multiplication.

Modular form 364650.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{11} - q^{12} - q^{13} + 4 q^{14} + q^{16} - q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.