Properties

Label 392784i
Number of curves $2$
Conductor $392784$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 392784i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
392784.i1 392784i1 \([0, -1, 0, -247319, -47238666]\) \(888770622281728/426952701\) \(803688933119184\) \([2]\) \(2150400\) \(1.8147\) \(\Gamma_0(N)\)-optimal
392784.i2 392784i2 \([0, -1, 0, -206404, -63424640]\) \(-32288802541648/39139035327\) \(-1178795101999673088\) \([2]\) \(4300800\) \(2.1613\)  

Rank

sage: E.rank()
 

The elliptic curves in class 392784i have rank \(0\).

Complex multiplication

The elliptic curves in class 392784i do not have complex multiplication.

Modular form 392784.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + q^{9} + 2 q^{15} - 6 q^{17} + O(q^{20})\) 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.