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Properties

Label 281775bo
Number of curves $2$
Conductor $281775$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bo1")
 
E.isogeny_class()
 

Elliptic curves in class 281775bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
281775.bo1 281775bo1 \([1, 1, 0, -4681525, -3900389000]\) \(147815204204011553/15178486401\) \(1165185995126765625\) \([2]\) \(6389760\) \(2.4995\) \(\Gamma_0(N)\)-optimal
281775.bo2 281775bo2 \([1, 1, 0, -4322400, -4523470875]\) \(-116340772335201233/47730591665289\) \(-3664068700805700890625\) \([2]\) \(12779520\) \(2.8461\)  

Rank

sage: E.rank()
 

The elliptic curves in class 281775bo have rank \(0\).

Complex multiplication

The elliptic curves in class 281775bo do not have complex multiplication.

Modular form 281775.2.a.bo

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.