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Properties

Label 116242.m
Number of curves $2$
Conductor $116242$
CM no
Rank $1$
Graph

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

Elliptic curves in class 116242.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116242.m1 116242f2 \([1, 1, 0, -10405110, -12536736172]\) \(2648147669062512625/90275612817152\) \(4247095737797807750912\) \([2]\) \(7741440\) \(2.9221\)  
116242.m2 116242f1 \([1, 1, 0, 222730, -682443436]\) \(25973783183375/4292763123712\) \(-201956823079343030272\) \([2]\) \(3870720\) \(2.5755\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 116242.m have rank \(1\).

Complex multiplication

The elliptic curves in class 116242.m do not have complex multiplication.

Modular form 116242.2.a.m

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