LMFDB - Elliptic curve isogeny class with Cremona label 490776bv (LMFDB label 490776.bv)

Properties

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Show commands: SageMath

sage:E = EllipticCurve("bv1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 490776bv have rank $1$.

The elliptic curves in class 490776bv 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.

$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$

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
490776.bv2	490776bv1	$[0, 1, 0, -42995, -3305106]$	$141150208/6561$	$408579138416592$	$[2]$	$3225600$	$1.5649$	$\Gamma_0(N)$-optimal
490776.bv1	490776bv2	$[0, 1, 0, -680060, -216084816]$	$34909201168/81$	$80706990304512$	$[2]$	$6451200$	$1.9114$

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Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
490776.bv2	490776bv1	\([0, 1, 0, -42995, -3305106]\)	\(141150208/6561\)	\(408579138416592\)	\([2]\)	\(3225600\)	\(1.5649\)	\(\Gamma_0(N)\)-optimal
490776.bv1	490776bv2	\([0, 1, 0, -680060, -216084816]\)	\(34909201168/81\)	\(80706990304512\)	\([2]\)	\(6451200\)	\(1.9114\)