Properties

Label 94192i
Number of curves $4$
Conductor $94192$
CM no
Rank $0$
Graph

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

Elliptic curves in class 94192i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
94192.r4 94192i1 [0, 0, 0, 841, -48778] [2] 96768 \(\Gamma_0(N)\)-optimal
94192.r3 94192i2 [0, 0, 0, -15979, -731670] [2, 2] 193536  
94192.r2 94192i3 [0, 0, 0, -49619, 3365682] [2] 387072  
94192.r1 94192i4 [0, 0, 0, -251459, -48534110] [2] 387072  

Rank

sage: E.rank()
 

The elliptic curves in class 94192i have rank \(0\).

Complex multiplication

The elliptic curves in class 94192i do not have complex multiplication.

Modular form 94192.2.a.i

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + q^{7} - 3q^{9} - 4q^{11} + 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.