Properties

Label 361b
Number of curves $3$
Conductor $361$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

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

Elliptic curves in class 361b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
361.b3 361b1 \([0, -1, 1, 241, -17]\) \(32768/19\) \(-893871739\) \([]\) \(120\) \(0.40705\) \(\Gamma_0(N)\)-optimal
361.b2 361b2 \([0, -1, 1, -3369, 81208]\) \(-89915392/6859\) \(-322687697779\) \([]\) \(360\) \(0.95635\)  
361.b1 361b3 \([0, -1, 1, -277729, 56427893]\) \(-50357871050752/19\) \(-893871739\) \([]\) \(1080\) \(1.5057\)  

Rank

sage: E.rank()
 

The elliptic curves in class 361b have rank \(0\).

Complex multiplication

The elliptic curves in class 361b do not have complex multiplication.

Modular form 361.2.a.b

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.