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Properties

Label 301530.n
Number of curves $2$
Conductor $301530$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 301530.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301530.n1 301530n2 \([1, 1, 0, -1057217, 417074421]\) \(882774443450089/2166000000\) \(320645735574000000\) \([2]\) \(8279040\) \(2.2373\)  
301530.n2 301530n1 \([1, 1, 0, -41537, 11411829]\) \(-53540005609/350208000\) \(-51843352614912000\) \([2]\) \(4139520\) \(1.8907\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 301530.n have rank \(1\).

Complex multiplication

The elliptic curves in class 301530.n do not have complex multiplication.

Modular form 301530.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 2 q^{7} - q^{8} + q^{9} - q^{10} - 4 q^{11} - q^{12} - 6 q^{13} - 2 q^{14} - q^{15} + q^{16} - 4 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.