LMFDB - Elliptic curve isogeny class with LMFDB label 705600.btp

Properties

Learn more

Show commands: SageMath

sage:E = EllipticCurve("btp1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 705600.btp have rank $1$.

The elliptic curves in class 705600.btp 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	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height
705600.btp1	$[0, 0, 0, -3615626700, -83499528294000]$	$551105805571803/1376829440$	$13059291747859908526080000000$	$[2]$	$743178240$	$4.2723$
705600.btp2	$[0, 0, 0, -2260874700, -146828765286000]$	$-134745327251163/903920796800$	$-8573731109620370413977600000000$	$[2]$	$1486356480$	$4.6189$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

LMFDB label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height
705600.btp1	\([0, 0, 0, -3615626700, -83499528294000]\)	\(551105805571803/1376829440\)	\(13059291747859908526080000000\)	\([2]\)	\(743178240\)	\(4.2723\)
705600.btp2	\([0, 0, 0, -2260874700, -146828765286000]\)	\(-134745327251163/903920796800\)	\(-8573731109620370413977600000000\)	\([2]\)	\(1486356480\)	\(4.6189\)