Properties

Label 3549.a
Number of curves $2$
Conductor $3549$
CM no
Rank $1$
Graph

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

Elliptic curves in class 3549.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3549.a1 3549b2 \([0, 1, 1, -64302, 6254642]\) \(-13383627864961024/151263\) \(-332324811\) \([]\) \(12000\) \(1.2032\)  
3549.a2 3549b1 \([0, 1, 1, 48, 1460]\) \(5451776/413343\) \(-908114571\) \([]\) \(2400\) \(0.39844\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3549.a have rank \(1\).

Complex multiplication

The elliptic curves in class 3549.a do not have complex multiplication.

Modular form 3549.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.