Properties

Label 17850s
Number of curves $4$
Conductor $17850$
CM no
Rank $1$
Graph

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

Elliptic curves in class 17850s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17850.y4 17850s1 \([1, 0, 1, 24, 12598]\) \(103823/4386816\) \(-68544000000\) \([2]\) \(24576\) \(0.75812\) \(\Gamma_0(N)\)-optimal
17850.y3 17850s2 \([1, 0, 1, -7976, 268598]\) \(3590714269297/73410624\) \(1147041000000\) \([2, 2]\) \(49152\) \(1.1047\)  
17850.y2 17850s3 \([1, 0, 1, -16976, -451402]\) \(34623662831857/14438442312\) \(225600661125000\) \([2]\) \(98304\) \(1.4513\)  
17850.y1 17850s4 \([1, 0, 1, -126976, 17404598]\) \(14489843500598257/6246072\) \(97594875000\) \([2]\) \(98304\) \(1.4513\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 17850.2.a.s

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