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Properties

Label 146523r
Number of curves $2$
Conductor $146523$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 146523r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
146523.x1 146523r1 \([1, 0, 1, -31647113, -68521589953]\) \(147815204204011553/15178486401\) \(359944335868917021417\) \([2]\) \(13418496\) \(2.9772\) \(\Gamma_0(N)\)-optimal
146523.x2 146523r2 \([1, 0, 1, -29219428, -79475304673]\) \(-116340772335201233/47730591665289\) \(-1131888626026704915851313\) \([2]\) \(26836992\) \(3.3238\)  

Rank

sage: E.rank()
 

The elliptic curves in class 146523r have rank \(0\).

Complex multiplication

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

Modular form 146523.2.a.r

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