Properties

Label 116886m
Number of curves $2$
Conductor $116886$
CM no
Rank $1$
Graph

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

Elliptic curves in class 116886m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.k2 116886m1 \([1, 0, 1, 360, -11618]\) \(2924207/34776\) \(-61607805336\) \([]\) \(172800\) \(0.75124\) \(\Gamma_0(N)\)-optimal
116886.k1 116886m2 \([1, 0, 1, -3270, 328150]\) \(-2181825073/25039686\) \(-44359331169846\) \([]\) \(518400\) \(1.3005\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116886m have rank \(1\).

Complex multiplication

The elliptic curves in class 116886m do not have complex multiplication.

Modular form 116886.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 3q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 3q^{10} + q^{12} - 5q^{13} + q^{14} - 3q^{15} + q^{16} - q^{18} - 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.