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Properties

Label 60690d
Number of curves $2$
Conductor $60690$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 60690d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60690.a2 60690d1 \([1, 1, 0, -5063, -209883]\) \(-594823321/428400\) \(-10340534559600\) \([2]\) \(147456\) \(1.1970\) \(\Gamma_0(N)\)-optimal
60690.a1 60690d2 \([1, 1, 0, -91763, -10735263]\) \(3540302642521/849660\) \(20508726876540\) \([2]\) \(294912\) \(1.5435\)  

Rank

sage: E.rank()
 

The elliptic curves in class 60690d have rank \(1\).

Complex multiplication

The elliptic curves in class 60690d do not have complex multiplication.

Modular form 60690.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.