Properties

Label 426a
Number of curves $2$
Conductor $426$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 426a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
426.c2 426a1 \([1, 0, 0, -20, 48]\) \(-887503681/552096\) \(-552096\) \([5]\) \(80\) \(-0.19647\) \(\Gamma_0(N)\)-optimal
426.c1 426a2 \([1, 0, 0, -230, -5202]\) \(-1345938541921/10825376106\) \(-10825376106\) \([]\) \(400\) \(0.60825\)  

Rank

sage: E.rank()
 

The elliptic curves in class 426a have rank \(0\).

Complex multiplication

The elliptic curves in class 426a do not have complex multiplication.

Modular form 426.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 3 q^{7} + q^{8} + q^{9} + q^{10} - 3 q^{11} + q^{12} - 6 q^{13} + 3 q^{14} + q^{15} + q^{16} - 2 q^{17} + q^{18} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.