Properties

Label 424830t
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 424830t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
424830.t1 424830t1 [1, 1, 0, -33198, 2377908] [] 2309472 \(\Gamma_0(N)\)-optimal
424830.t2 424830t2 [1, 1, 0, 154227, 8862813] [] 6928416  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 424830.2.a.t

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

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.