Properties

Label 301530v
Number of curves $2$
Conductor $301530$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 301530v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301530.v2 301530v1 \([1, 0, 1, -1395249, -597711164]\) \(2029137179059801/132118594560\) \(19558293599120163840\) \([2]\) \(10137600\) \(2.4516\) \(\Gamma_0(N)\)-optimal
301530.v1 301530v2 \([1, 0, 1, -21962769, -39618410108]\) \(7914399140778079321/37124373600\) \(5495739649444130400\) \([2]\) \(20275200\) \(2.7982\)  

Rank

sage: E.rank()
 

The elliptic curves in class 301530v have rank \(0\).

Complex multiplication

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

Modular form 301530.2.a.v

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