Properties

Label 192556i
Number of curves $2$
Conductor $192556$
CM no
Rank $0$
Graph

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

Elliptic curves in class 192556i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
192556.j2 192556i1 \([0, 0, 0, -116380, 15220917]\) \(73598976000/336973\) \(798145561983952\) \([2]\) \(760320\) \(1.7103\) \(\Gamma_0(N)\)-optimal
192556.j1 192556i2 \([0, 0, 0, -177215, -2409066]\) \(16241202000/9332687\) \(353682589901758208\) \([2]\) \(1520640\) \(2.0569\)  

Rank

sage: E.rank()
 

The elliptic curves in class 192556i have rank \(0\).

Complex multiplication

The elliptic curves in class 192556i do not have complex multiplication.

Modular form 192556.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{7} - 3q^{9} - q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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 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.