Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ey1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 364650.ey

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.ey1 364650ey3 \([1, 1, 1, -82380513, -287781855969]\) \(3957101249824708884951625/772310238681366528\) \(12067347479396352000000\) \([2]\) \(65691648\) \(3.2368\)  
364650.ey2 364650ey4 \([1, 1, 1, -73676513, -350955487969]\) \(-2830680648734534916567625/1766676274677722124288\) \(-27604316791839408192000000\) \([2]\) \(131383296\) \(3.5834\)  
364650.ey3 364650ey1 \([1, 1, 1, -2508138, 988967031]\) \(111675519439697265625/37528570137307392\) \(586383908395428000000\) \([2]\) \(21897216\) \(2.6875\) \(\Gamma_0(N)\)-optimal
364650.ey4 364650ey2 \([1, 1, 1, 7317862, 6845263031]\) \(2773679829880629422375/2899504554614368272\) \(-45304758665849504250000\) \([2]\) \(43794432\) \(3.0341\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 364650.2.a.ey

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.