Properties

Label 5850.g
Number of curves $4$
Conductor $5850$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5850.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5850.g1 5850j4 \([1, -1, 0, -196329942, 1058876009716]\) \(73474353581350183614361/576510977802240\) \(6566820356528640000000\) \([2]\) \(829440\) \(3.3594\)  
5850.g2 5850j3 \([1, -1, 0, -12009942, 17283689716]\) \(-16818951115904497561/1592332281446400\) \(-18137659893350400000000\) \([2]\) \(414720\) \(3.0128\)  
5850.g3 5850j2 \([1, -1, 0, -3600567, -98094659]\) \(453198971846635561/261896250564000\) \(2983161979080562500000\) \([2]\) \(276480\) \(2.8101\)  
5850.g4 5850j1 \([1, -1, 0, 899433, -12594659]\) \(7064514799444439/4094064000000\) \(-46633947750000000000\) \([2]\) \(138240\) \(2.4635\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5850.g have rank \(0\).

Complex multiplication

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

Modular form 5850.2.a.g

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.