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Properties

Label 17850ba
Number of curves $2$
Conductor $17850$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 17850ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17850.u2 17850ba1 \([1, 0, 1, 3174, 400048]\) \(9056932295/181997172\) \(-71092645312500\) \([3]\) \(64800\) \(1.3383\) \(\Gamma_0(N)\)-optimal
17850.u1 17850ba2 \([1, 0, 1, -28701, -11074952]\) \(-6693187811305/131714173248\) \(-51450848925000000\) \([]\) \(194400\) \(1.8876\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17850ba have rank \(1\).

Complex multiplication

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

Modular form 17850.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} - 6 q^{11} + q^{12} - 4 q^{13} - q^{14} + q^{16} + q^{17} - q^{18} - q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.