Properties

Label 6630.s
Number of curves $2$
Conductor $6630$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 6630.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6630.s1 6630q1 \([1, 1, 1, -13620, 599157]\) \(279419703685750081/3666124800000\) \(3666124800000\) \([2]\) \(15360\) \(1.2185\) \(\Gamma_0(N)\)-optimal
6630.s2 6630q2 \([1, 1, 1, -2100, 1594485]\) \(-1024222994222401/1098922500000000\) \(-1098922500000000\) \([2]\) \(30720\) \(1.5651\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6630.s have rank \(1\).

Complex multiplication

The elliptic curves in class 6630.s do not have complex multiplication.

Modular form 6630.2.a.s

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