LMFDB - Elliptic curve isogeny class with LMFDB label 450800.bt (Cremona label 450800bt)

Properties

Learn more

Show commands: SageMath

sage:E = EllipticCurve("bt1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 450800.bt have rank $0$.

The elliptic curves in class 450800.bt do not have complex multiplication.

sage:E.q_eigenform(10)

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.

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

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

The vertices are labelled with LMFDB labels.

sage:E.isogeny_class().curves

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
450800.bt1	450800bt1	$[0, 1, 0, -54308, -3908612]$	$109744/23$	$3712531844000000$	$[2]$	$2752512$	$1.7024$	$\Gamma_0(N)$-optimal
450800.bt2	450800bt2	$[0, 1, 0, 117192, -23459612]$	$275684/529$	$-341552929648000000$	$[2]$	$5505024$	$2.0489$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
450800.bt1	450800bt1	\([0, 1, 0, -54308, -3908612]\)	\(109744/23\)	\(3712531844000000\)	\([2]\)	\(2752512\)	\(1.7024\)	\(\Gamma_0(N)\)-optimal
450800.bt2	450800bt2	\([0, 1, 0, 117192, -23459612]\)	\(275684/529\)	\(-341552929648000000\)	\([2]\)	\(5505024\)	\(2.0489\)