Properties

Label 1470.q
Number of curves $6$
Conductor $1470$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 1470.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1470.q1 1470p5 \([1, 0, 0, -823201, 287410955]\) \(524388516989299201/3150\) \(370594350\) \([2]\) \(12288\) \(1.7097\)  
1470.q2 1470p4 \([1, 0, 0, -51451, 4487405]\) \(128031684631201/9922500\) \(1167372202500\) \([2, 2]\) \(6144\) \(1.3631\)  
1470.q3 1470p6 \([1, 0, 0, -48021, 5112351]\) \(-104094944089921/35880468750\) \(-4221301267968750\) \([2]\) \(12288\) \(1.7097\)  
1470.q4 1470p3 \([1, 0, 0, -18131, -889659]\) \(5602762882081/345888060\) \(40693384370940\) \([2]\) \(6144\) \(1.3631\)  
1470.q5 1470p2 \([1, 0, 0, -3431, 59961]\) \(37966934881/8643600\) \(1016910896400\) \([2, 2]\) \(3072\) \(1.0166\)  
1470.q6 1470p1 \([1, 0, 0, 489, 5865]\) \(109902239/188160\) \(-22136835840\) \([2]\) \(1536\) \(0.66999\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1470.q have rank \(0\).

Complex multiplication

The elliptic curves in class 1470.q do not have complex multiplication.

Modular form 1470.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} + 4 q^{11} + q^{12} + 2 q^{13} - q^{15} + q^{16} - 2 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.