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Properties

Label 60690o
Number of curves $2$
Conductor $60690$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 60690o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60690.m1 60690o1 \([1, 1, 0, -1612, 153424]\) \(-1604507946409/34566497280\) \(-9989717713920\) \([]\) \(155520\) \(1.1752\) \(\Gamma_0(N)\)-optimal
60690.m2 60690o2 \([1, 1, 0, 14453, -4058819]\) \(1155188682445031/25367150592000\) \(-7331106521088000\) \([]\) \(466560\) \(1.7245\)  

Rank

sage: E.rank()
 

The elliptic curves in class 60690o have rank \(0\).

Complex multiplication

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

Modular form 60690.2.a.o

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.