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Properties

Label 275550bp
Number of curves $2$
Conductor $275550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 275550bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
275550.bp2 275550bp1 \([1, 1, 1, -39888, -5008719]\) \(-449191107501625/429068648448\) \(-6704197632000000\) \([2]\) \(1492992\) \(1.7330\) \(\Gamma_0(N)\)-optimal
275550.bp1 275550bp2 \([1, 1, 1, -743888, -247184719]\) \(2913576204142509625/1030541833728\) \(16102216152000000\) \([2]\) \(2985984\) \(2.0796\)  

Rank

sage: E.rank()
 

The elliptic curves in class 275550bp have rank \(1\).

Complex multiplication

The elliptic curves in class 275550bp do not have complex multiplication.

Modular form 275550.2.a.bp

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.