Properties

Label 424830.t
Number of curves $2$
Conductor $424830$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 424830.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
424830.t1 424830t1 \([1, 1, 0, -33198, 2377908]\) \(-5831629329001/186624000\) \(-129496340736000\) \([]\) \(2309472\) \(1.4837\) \(\Gamma_0(N)\)-optimal
424830.t2 424830t2 \([1, 1, 0, 154227, 8862813]\) \(584669638645799/386547056640\) \(-268220750584872960\) \([]\) \(6928416\) \(2.0330\)  

Rank

sage: E.rank()
 

The elliptic curves in class 424830.t have rank \(1\).

Complex multiplication

The elliptic curves in class 424830.t do not have complex multiplication.

Modular form 424830.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} + 3q^{11} - q^{12} + 2q^{13} + q^{15} + q^{16} - q^{18} + 5q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.