Properties

Label 393008j
Number of curves $2$
Conductor $393008$
CM no
Rank $1$
Graph

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

Elliptic curves in class 393008j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
393008.j2 393008j1 \([0, 1, 0, -18432, 1007092]\) \(-95443993/5887\) \(-42717919670272\) \([2]\) \(983040\) \(1.3699\) \(\Gamma_0(N)\)-optimal
393008.j1 393008j2 \([0, 1, 0, -299152, 62877780]\) \(408023180713/1421\) \(10311221989376\) \([2]\) \(1966080\) \(1.7165\)  

Rank

sage: E.rank()
 

The elliptic curves in class 393008j have rank \(1\).

Complex multiplication

The elliptic curves in class 393008j do not have complex multiplication.

Modular form 393008.2.a.j

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + 2 q^{5} + q^{7} + q^{9} + 2 q^{13} - 4 q^{15} - 4 q^{17} + 2 q^{19} + O(q^{20})\) 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.