Properties

Label 46090i
Number of curves $2$
Conductor $46090$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 46090i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46090.p1 46090i1 \([1, -1, 1, -93, -319]\) \(88061730849/460900\) \(460900\) \([2]\) \(6048\) \(-0.068075\) \(\Gamma_0(N)\)-optimal
46090.p2 46090i2 \([1, -1, 1, -43, -699]\) \(-8602523649/212428810\) \(-212428810\) \([2]\) \(12096\) \(0.27850\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46090i have rank \(1\).

Complex multiplication

The elliptic curves in class 46090i do not have complex multiplication.

Modular form 46090.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{8} - 3 q^{9} - q^{10} + q^{11} - 2 q^{13} + q^{16} + 6 q^{17} - 3 q^{18} - 4 q^{19} + O(q^{20})\) 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 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.