↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 6630m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6630.o2 6630m1 \([1, 0, 1, -293, -2194]\) \(-2768178670921/431115750\) \(-431115750\) \([3]\) \(3456\) \(0.38552\) \(\Gamma_0(N)\)-optimal
6630.o1 6630m2 \([1, 0, 1, -24518, -1479664]\) \(-1629871520330191321/4481880\) \(-4481880\) \([]\) \(10368\) \(0.93483\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6630.2.a.m

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.