Properties

Label 441.b
Number of curves $2$
Conductor $441$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 441.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
441.b1 441e2 \([0, 0, 1, -402339, 98307144]\) \(-1713910976512/1594323\) \(-6700206067223067\) \([]\) \(4368\) \(1.9596\)  
441.b2 441e1 \([0, 0, 1, -1029, -13806]\) \(-28672/3\) \(-12607619787\) \([]\) \(336\) \(0.67717\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 441.b have rank \(0\).

Complex multiplication

The elliptic curves in class 441.b do not have complex multiplication.

Modular form 441.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2q^{2} + 2q^{4} + 2q^{5} - 4q^{10} + 2q^{11} + q^{13} - 4q^{16} + q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.