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Properties

Label 60690.l
Number of curves $4$
Conductor $60690$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 60690.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60690.l1 60690j4 \([1, 1, 0, -1080201808, -13665255280352]\) \(5774905528848578698851241/31070538632700000\) \(749967270113961906300000\) \([2]\) \(33177600\) \(3.7757\)  
60690.l2 60690j3 \([1, 1, 0, -217270928, 985627537632]\) \(46993202771097749198761/9805297851562500000\) \(236676053457641601562500000\) \([2]\) \(33177600\) \(3.7757\)  
60690.l3 60690j2 \([1, 1, 0, -68701808, -205629380352]\) \(1485712211163154851241/103233690000000000\) \(2491810315499610000000000\) \([2, 2]\) \(16588800\) \(3.4291\)  
60690.l4 60690j1 \([1, 1, 0, 3802512, -13913457408]\) \(251907898698209879/3611226931200000\) \(-87166239226498252800000\) \([2]\) \(8294400\) \(3.0825\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 60690.2.a.l

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.