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Properties

Label 56350.bo
Number of curves $2$
Conductor $56350$
CM no
Rank $1$
Graph

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

Elliptic curves in class 56350.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56350.bo1 56350bg1 \([1, -1, 1, -79855, -4641353]\) \(89314623/36800\) \(23203324025000000\) \([2]\) \(387072\) \(1.8377\) \(\Gamma_0(N)\)-optimal
56350.bo2 56350bg2 \([1, -1, 1, 263145, -34139353]\) \(3196010817/2645000\) \(-1667738914296875000\) \([2]\) \(774144\) \(2.1842\)  

Rank

sage: E.rank()
 

The elliptic curves in class 56350.bo have rank \(1\).

Complex multiplication

The elliptic curves in class 56350.bo do not have complex multiplication.

Modular form 56350.2.a.bo

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} - 3 q^{9} - 2 q^{11} - 2 q^{13} + q^{16} + 2 q^{17} - 3 q^{18} + 4 q^{19} + O(q^{20})\) 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 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.