Properties

Label 1530.b
Number of curves $8$
Conductor $1530$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1530.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1530.b1 1530c7 [1, -1, 0, -1021230, 397475626] [2] 16384  
1530.b2 1530c3 [1, -1, 0, -195840, -33309104] [2] 4096  
1530.b3 1530c5 [1, -1, 0, -64980, 5986876] [2, 2] 8192  
1530.b4 1530c4 [1, -1, 0, -12960, -453200] [2, 2] 4096  
1530.b5 1530c2 [1, -1, 0, -12240, -518144] [2, 2] 2048  
1530.b6 1530c1 [1, -1, 0, -720, -8960] [2] 1024 \(\Gamma_0(N)\)-optimal
1530.b7 1530c6 [1, -1, 0, 27540, -2745500] [2] 8192  
1530.b8 1530c8 [1, -1, 0, 58950, 26038750] [2] 16384  

Rank

sage: E.rank()
 

The elliptic curves in class 1530.b have rank \(0\).

Complex multiplication

The elliptic curves in class 1530.b do not have complex multiplication.

Modular form 1530.2.a.b

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 16 & 8 & 4 \\ 16 & 1 & 8 & 4 & 2 & 4 & 8 & 16 \\ 2 & 8 & 1 & 2 & 4 & 8 & 4 & 2 \\ 4 & 4 & 2 & 1 & 2 & 4 & 2 & 4 \\ 8 & 2 & 4 & 2 & 1 & 2 & 4 & 8 \\ 16 & 4 & 8 & 4 & 2 & 1 & 8 & 16 \\ 8 & 8 & 4 & 2 & 4 & 8 & 1 & 8 \\ 4 & 16 & 2 & 4 & 8 & 16 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.