# Properties

 Label 46800y Number of curves $4$ Conductor $46800$ CM no Rank $0$ Graph

# Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 46800y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.q3 46800y1 $$[0, 0, 0, -25050, 1522375]$$ $$9538484224/26325$$ $$4797731250000$$ $$[2]$$ $$147456$$ $$1.3062$$ $$\Gamma_0(N)$$-optimal
46800.q2 46800y2 $$[0, 0, 0, -35175, 175750]$$ $$1650587344/950625$$ $$2772022500000000$$ $$[2, 2]$$ $$294912$$ $$1.6528$$
46800.q4 46800y3 $$[0, 0, 0, 140325, 1404250]$$ $$26198797244/15234375$$ $$-177693750000000000$$ $$[2]$$ $$589824$$ $$1.9993$$
46800.q1 46800y4 $$[0, 0, 0, -372675, -87236750]$$ $$490757540836/2142075$$ $$24985162800000000$$ $$[2]$$ $$589824$$ $$1.9993$$

## Rank

sage: E.rank()

The elliptic curves in class 46800y have rank $$0$$.

## Complex multiplication

The elliptic curves in class 46800y do not have complex multiplication.

## Modular form 46800.2.a.y

sage: E.q_eigenform(10)

$$q - 4q^{7} + 4q^{11} - q^{13} - 6q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.