# Properties

 Label 17850.y Number of curves $4$ Conductor $17850$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 17850.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17850.y1 17850s4 $$[1, 0, 1, -126976, 17404598]$$ $$14489843500598257/6246072$$ $$97594875000$$ $$$$ $$98304$$ $$1.4513$$
17850.y2 17850s3 $$[1, 0, 1, -16976, -451402]$$ $$34623662831857/14438442312$$ $$225600661125000$$ $$$$ $$98304$$ $$1.4513$$
17850.y3 17850s2 $$[1, 0, 1, -7976, 268598]$$ $$3590714269297/73410624$$ $$1147041000000$$ $$[2, 2]$$ $$49152$$ $$1.1047$$
17850.y4 17850s1 $$[1, 0, 1, 24, 12598]$$ $$103823/4386816$$ $$-68544000000$$ $$$$ $$24576$$ $$0.75812$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 17850.y have rank $$1$$.

## Complex multiplication

The elliptic curves in class 17850.y do not have complex multiplication.

## Modular form 17850.2.a.y

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} + q^{12} + 6q^{13} - q^{14} + q^{16} - q^{17} - q^{18} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 