LMFDB - Elliptic curve isogeny class with LMFDB label 412200.k (Cremona label 412200k)

Properties

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Show commands: SageMath

sage:E = EllipticCurve("k1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 412200.k have rank $1$.

The elliptic curves in class 412200.k 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
412200.k1	412200k1	$[0, 0, 0, -16050, 768625]$	$2508888064/51525$	$9390431250000$	$[2]$	$761856$	$1.2797$	$\Gamma_0(N)$-optimal
412200.k2	412200k2	$[0, 0, 0, 825, 2304250]$	$21296/786615$	$-2293769340000000$	$[2]$	$1523712$	$1.6263$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
412200.k1	412200k1	\([0, 0, 0, -16050, 768625]\)	\(2508888064/51525\)	\(9390431250000\)	\([2]\)	\(761856\)	\(1.2797\)	\(\Gamma_0(N)\)-optimal
412200.k2	412200k2	\([0, 0, 0, 825, 2304250]\)	\(21296/786615\)	\(-2293769340000000\)	\([2]\)	\(1523712\)	\(1.6263\)