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Properties

Label 60690g
Number of curves $2$
Conductor $60690$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 60690g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60690.i2 60690g1 \([1, 1, 0, -898, -97292]\) \(-16329068153/816480000\) \(-4011366240000\) \([2]\) \(147456\) \(1.0983\) \(\Gamma_0(N)\)-optimal
60690.i1 60690g2 \([1, 1, 0, -37618, -2807228]\) \(1198345620520313/8268750000\) \(40624368750000\) \([2]\) \(294912\) \(1.4449\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 60690.2.a.g

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