Properties

Label 361920.bb
Number of curves $2$
Conductor $361920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 361920.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
361920.bb1 361920bb1 \([0, -1, 0, -53281, 4044961]\) \(63812982460681/10201800960\) \(2674340910858240\) \([2]\) \(1474560\) \(1.6826\) \(\Gamma_0(N)\)-optimal
361920.bb2 361920bb2 \([0, -1, 0, 95199, 22426785]\) \(363979050334199/1041836936400\) \(-273111301855641600\) \([2]\) \(2949120\) \(2.0292\)  

Rank

sage: E.rank()
 

The elliptic curves in class 361920.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 361920.bb do not have complex multiplication.

Modular form 361920.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} + 4 q^{11} + q^{13} + q^{15} - 4 q^{17} + O(q^{20})\)  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 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.