↑

Properties

Label 27930.cl
Number of curves $2$
Conductor $27930$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cl1")
 
E.isogeny_class()
 

Elliptic curves in class 27930.cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27930.cl1 27930cq2 \([1, 1, 1, -1142975, 469854335]\) \(1403607530712116449/39475350\) \(4644235452150\) \([2]\) \(403200\) \(1.9410\)  
27930.cl2 27930cq1 \([1, 1, 1, -71345, 7338827]\) \(-341370886042369/1817528220\) \(-213830377554780\) \([2]\) \(201600\) \(1.5945\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 27930.cl have rank \(0\).

Complex multiplication

The elliptic curves in class 27930.cl do not have complex multiplication.

Modular form 27930.2.a.cl

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