↑

Properties

Label 364650.m
Number of curves $2$
Conductor $364650$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 364650.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.m1 364650m2 \([1, 1, 0, -18980, -1014000]\) \(6049759017137597/2785109184\) \(348138648000\) \([2]\) \(884736\) \(1.1714\)  
364650.m2 364650m1 \([1, 1, 0, -1380, -10800]\) \(2327783545277/985780224\) \(123222528000\) \([2]\) \(442368\) \(0.82485\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 364650.m have rank \(2\).

Complex multiplication

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

Modular form 364650.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 2 q^{7} - q^{8} + q^{9} + q^{11} - q^{12} - q^{13} + 2 q^{14} + q^{16} + q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.