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Properties

Label 146523i
Number of curves $2$
Conductor $146523$
CM no
Rank $1$
Graph

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

Elliptic curves in class 146523i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
146523.d2 146523i1 \([0, -1, 1, 276766, -28975828]\) \(4096/3\) \(-1717203088699824219\) \([]\) \(3818880\) \(2.1872\) \(\Gamma_0(N)\)-optimal
146523.d1 146523i2 \([0, -1, 1, -41238084, -101916381292]\) \(-13549359104/243\) \(-139093450184685761739\) \([]\) \(19094400\) \(2.9920\)  

Rank

sage: E.rank()
 

The elliptic curves in class 146523i have rank \(1\).

Complex multiplication

The elliptic curves in class 146523i do not have complex multiplication.

Modular form 146523.2.a.i

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} - q^{3} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + q^{9} - 6 q^{10} + 5 q^{11} - 2 q^{12} + 4 q^{14} - 3 q^{15} - 4 q^{16} - 2 q^{18} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.