Properties

Label 23826m
Number of curves $2$
Conductor $23826$
CM no
Rank $0$
Graph

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

Elliptic curves in class 23826m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23826.p2 23826m1 \([1, 0, 1, -685186, -269272984]\) \(-2094688437625/631351908\) \(-10722604930573632228\) \([3]\) \(492480\) \(2.3656\) \(\Gamma_0(N)\)-optimal
23826.p1 23826m2 \([1, 0, 1, -59020981, -174529959808]\) \(-1338795256993539625/20699712\) \(-351554863682544192\) \([]\) \(1477440\) \(2.9149\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23826m have rank \(0\).

Complex multiplication

The elliptic curves in class 23826m do not have complex multiplication.

Modular form 23826.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - q^{11} + q^{12} - 4 q^{13} + q^{14} + q^{16} - 3 q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.