Properties

Label 114950.m
Number of curves $3$
Conductor $114950$
CM no
Rank $0$
Graph

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

Elliptic curves in class 114950.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
114950.m1 114950m3 \([1, 1, 0, -258700, 407282000]\) \(-69173457625/2550136832\) \(-70589421191168000000\) \([]\) \(2799360\) \(2.4888\)  
114950.m2 114950m1 \([1, 1, 0, -46950, -3936500]\) \(-413493625/152\) \(-4207457375000\) \([]\) \(311040\) \(1.3902\) \(\Gamma_0(N)\)-optimal
114950.m3 114950m2 \([1, 1, 0, 28675, -14871875]\) \(94196375/3511808\) \(-97209095192000000\) \([]\) \(933120\) \(1.9395\)  

Rank

sage: E.rank()
 

The elliptic curves in class 114950.m have rank \(0\).

Complex multiplication

The elliptic curves in class 114950.m do not have complex multiplication.

Modular form 114950.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} - 2 q^{9} - q^{12} + 5 q^{13} + q^{14} + q^{16} + 3 q^{17} + 2 q^{18} - q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.