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Properties

Label 17238.m
Number of curves $2$
Conductor $17238$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 17238.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17238.m1 17238j1 \([1, 1, 1, -426, 1971]\) \(1771561/612\) \(2954007108\) \([2]\) \(15360\) \(0.51895\) \(\Gamma_0(N)\)-optimal
17238.m2 17238j2 \([1, 1, 1, 1264, 15491]\) \(46268279/46818\) \(-225981543762\) \([2]\) \(30720\) \(0.86552\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17238.m have rank \(0\).

Complex multiplication

The elliptic curves in class 17238.m do not have complex multiplication.

Modular form 17238.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 4 q^{5} - q^{6} + 2 q^{7} + q^{8} + q^{9} + 4 q^{10} - q^{12} + 2 q^{14} - 4 q^{15} + q^{16} - q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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.