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Properties

Label 166635m
Number of curves $2$
Conductor $166635$
CM no
Rank $1$
Graph

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

Elliptic curves in class 166635m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166635.p1 166635m1 \([1, -1, 1, -6844037, -6869697676]\) \(328523283207001/1109390625\) \(119723398389282515625\) \([2]\) \(4866048\) \(2.7167\) \(\Gamma_0(N)\)-optimal
166635.p2 166635m2 \([1, -1, 1, -3868412, -12882840676]\) \(-59323563117001/630142750125\) \(-68003848072299583135125\) \([2]\) \(9732096\) \(3.0633\)  

Rank

sage: E.rank()
 

The elliptic curves in class 166635m have rank \(1\).

Complex multiplication

The elliptic curves in class 166635m do not have complex multiplication.

Modular form 166635.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} + q^{7} + 3 q^{8} - q^{10} - 2 q^{11} - q^{14} - q^{16} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.