LMFDB - Elliptic curve isogeny class with Cremona label 462400co (LMFDB label 462400.co)

Properties

Learn more

Show commands: SageMath

sage:E = EllipticCurve("co1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 462400co have rank $1$.

The elliptic curves in class 462400co 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 Cremona numbering.

$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$

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

The vertices are labelled with Cremona labels.

sage:E.isogeny_class().curves

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
462400.co1	462400co1	$[0, -1, 0, -23233, 1373537]$	$-1723025/4$	$-3219783680000$	$[]$	$737280$	$1.2808$	$\Gamma_0(N)$-optimal
462400.co2	462400co2	$[0, -1, 0, 167167, -22426463]$	$1026895/1024$	$-515165388800000000$	$[]$	$3686400$	$2.0855$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
462400.co1	462400co1	\([0, -1, 0, -23233, 1373537]\)	\(-1723025/4\)	\(-3219783680000\)	\([]\)	\(737280\)	\(1.2808\)	\(\Gamma_0(N)\)-optimal
462400.co2	462400co2	\([0, -1, 0, 167167, -22426463]\)	\(1026895/1024\)	\(-515165388800000000\)	\([]\)	\(3686400\)	\(2.0855\)