# Properties

 Label 47190k Number of curves $6$ Conductor $47190$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 47190k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.n6 47190k1 $$[1, 1, 0, 1813, -11139]$$ $$371694959/249600$$ $$-442181625600$$ $$$$ $$81920$$ $$0.92330$$ $$\Gamma_0(N)$$-optimal
47190.n5 47190k2 $$[1, 1, 0, -7867, -102131]$$ $$30400540561/15210000$$ $$26945442810000$$ $$[2, 2]$$ $$163840$$ $$1.2699$$
47190.n3 47190k3 $$[1, 1, 0, -68367, 6782769]$$ $$19948814692561/231344100$$ $$409840185140100$$ $$[2, 2]$$ $$327680$$ $$1.6164$$
47190.n2 47190k4 $$[1, 1, 0, -102247, -12616919]$$ $$66730743078481/60937500$$ $$107954498437500$$ $$$$ $$327680$$ $$1.6164$$
47190.n4 47190k5 $$[1, 1, 0, -13917, 17356959]$$ $$-168288035761/73415764890$$ $$-130060505864293290$$ $$$$ $$655360$$ $$1.9630$$
47190.n1 47190k6 $$[1, 1, 0, -1090817, 438052179]$$ $$81025909800741361/11088090$$ $$19643227808490$$ $$$$ $$655360$$ $$1.9630$$

## Rank

sage: E.rank()

The elliptic curves in class 47190k have rank $$1$$.

## Complex multiplication

The elliptic curves in class 47190k do not have complex multiplication.

## Modular form 47190.2.a.k

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - q^{12} - q^{13} - q^{15} + q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20})$$ ## Isogeny matrix

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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 