LMFDB - Elliptic curve isogeny class with LMFDB label 470400.di (Cremona label 470400di)

Properties

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Show commands: SageMath

sage:E = EllipticCurve("di1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 470400.di have rank $1$.

The elliptic curves in class 470400.di 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
470400.di1	470400di1	$[0, -1, 0, -203758, 35457262]$	$3976047968/1575$	$370594350000000$	$[2]$	$2359296$	$1.7597$	$\Gamma_0(N)$-optimal
470400.di2	470400di2	$[0, -1, 0, -173133, 46451637]$	$-19056256/19845$	$-597694567680000000$	$[2]$	$4718592$	$2.1063$

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Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
470400.di1	470400di1	\([0, -1, 0, -203758, 35457262]\)	\(3976047968/1575\)	\(370594350000000\)	\([2]\)	\(2359296\)	\(1.7597\)	\(\Gamma_0(N)\)-optimal
470400.di2	470400di2	\([0, -1, 0, -173133, 46451637]\)	\(-19056256/19845\)	\(-597694567680000000\)	\([2]\)	\(4718592\)	\(2.1063\)