Properties

Label 2420a
Number of curves 2
Conductor 2420
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2420.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2420a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2420.d2 2420a1 [0, 0, 0, -10648, 483153] [2] 6336 \(\Gamma_0(N)\)-optimal
2420.d1 2420a2 [0, 0, 0, -177023, 28667078] [2] 12672  

Rank

sage: E.rank()
 

The elliptic curves in class 2420a have rank \(0\).

Modular form 2420.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{5} + 4q^{7} - 3q^{9} + 4q^{13} - 4q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.