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Properties

Label 1530.p
Number of curves $2$
Conductor $1530$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 1530.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1530.p1 1530o2 \([1, -1, 1, -415742, -103064691]\) \(10901014250685308569/1040774054400\) \(758724285657600\) \([2]\) \(16128\) \(1.8919\)  
1530.p2 1530o1 \([1, -1, 1, -24062, -1854579]\) \(-2113364608155289/828431400960\) \(-603926491299840\) \([2]\) \(8064\) \(1.5453\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1530.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + 2 q^{7} + q^{8} + q^{10} + 4 q^{11} + 4 q^{13} + 2 q^{14} + q^{16} - q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.