Properties

Label 5850.s
Number of curves $2$
Conductor $5850$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 5850.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.s1 5850p2 \([1, -1, 0, -191817, 32383341]\) \(68523370149961/243360\) \(2772022500000\) \([2]\) \(30720\) \(1.6059\)  
5850.s2 5850p1 \([1, -1, 0, -11817, 523341]\) \(-16022066761/998400\) \(-11372400000000\) \([2]\) \(15360\) \(1.2593\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5850.s have rank \(1\).

Complex multiplication

The elliptic curves in class 5850.s do not have complex multiplication.

Modular form 5850.2.a.s

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