Properties

Label 63536.bd
Number of curves $2$
Conductor $63536$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 63536.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63536.bd1 63536t1 \([0, 1, 0, -157877, 28184099]\) \(-2258403328/480491\) \(-92590581381410816\) \([]\) \(622080\) \(1.9769\) \(\Gamma_0(N)\)-optimal
63536.bd2 63536t2 \([0, 1, 0, 1112843, -162932189]\) \(790939860992/517504691\) \(-99723116993444950016\) \([]\) \(1866240\) \(2.5263\)  

Rank

sage: E.rank()
 

The elliptic curves in class 63536.bd have rank \(1\).

Complex multiplication

The elliptic curves in class 63536.bd do not have complex multiplication.

Modular form 63536.2.a.bd

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.