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Properties

Label 17850.g
Number of curves $2$
Conductor $17850$
CM no
Rank $0$
Graph

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

Elliptic curves in class 17850.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17850.g1 17850c2 \([1, 1, 0, -6400, -204290]\) \(-1159924308480625/31212514998\) \(-780312874950\) \([]\) \(31104\) \(1.0638\)  
17850.g2 17850c1 \([1, 1, 0, 350, -980]\) \(188819819375/131167512\) \(-3279187800\) \([]\) \(10368\) \(0.51446\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 17850.g have rank \(0\).

Complex multiplication

The elliptic curves in class 17850.g do not have complex multiplication.

Modular form 17850.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} - q^{12} + 4 q^{13} + q^{14} + q^{16} + q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.