LMFDB - Elliptic curve isogeny class with LMFDB label 486720.ft (Cremona label 486720ft)

Properties

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Show commands: SageMath

sage:E = EllipticCurve("ft1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 486720.ft have rank $1$.

The elliptic curves in class 486720.ft 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
486720.ft1	486720ft1	$[0, 0, 0, -14703, 623948]$	$42144192/4225$	$35239567147200$	$[2]$	$1032192$	$1.3357$	$\Gamma_0(N)$-optimal
486720.ft2	486720ft2	$[0, 0, 0, 18252, 3023072]$	$1259712/8125$	$-4337177495040000$	$[2]$	$2064384$	$1.6823$

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Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
486720.ft1	486720ft1	\([0, 0, 0, -14703, 623948]\)	\(42144192/4225\)	\(35239567147200\)	\([2]\)	\(1032192\)	\(1.3357\)	\(\Gamma_0(N)\)-optimal
486720.ft2	486720ft2	\([0, 0, 0, 18252, 3023072]\)	\(1259712/8125\)	\(-4337177495040000\)	\([2]\)	\(2064384\)	\(1.6823\)