Properties

Label 364650j
Number of curves $2$
Conductor $364650$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 364650j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.j1 364650j1 \([1, 1, 0, -7130200, -6291896000]\) \(20525743802277925973/3130368760037376\) \(6114001484448000000000\) \([2]\) \(27955200\) \(2.9042\) \(\Gamma_0(N)\)-optimal
364650.j2 364650j2 \([1, 1, 0, 12309800, -34577096000]\) \(105620108359694738347/325643393533670784\) \(-636022252995450750000000\) \([2]\) \(55910400\) \(3.2507\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 364650.2.a.j

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.