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Properties

Label 350727.j
Number of curves $2$
Conductor $350727$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 350727.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350727.j1 350727j2 \([1, 1, 0, -256840, 27071287]\) \(12657482097625/5169365253\) \(765251580793564917\) \([2]\) \(4866048\) \(2.1292\)  
350727.j2 350727j1 \([1, 1, 0, 52625, 3118696]\) \(108872984375/90990783\) \(-13469901452211087\) \([2]\) \(2433024\) \(1.7826\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 350727.j have rank \(0\).

Complex multiplication

The elliptic curves in class 350727.j do not have complex multiplication.

Modular form 350727.2.a.j

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