# Properties

 Label 254100.by Number of curves $2$ Conductor $254100$ CM no Rank $2$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("by1")

sage: E.isogeny_class()

## Elliptic curves in class 254100.by

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254100.by1 254100by2 $$[0, 1, 0, -1561908, -750526812]$$ $$59466754384/121275$$ $$859384241100000000$$ $$$$ $$5529600$$ $$2.3277$$
254100.by2 254100by1 $$[0, 1, 0, -64533, -19807812]$$ $$-67108864/343035$$ $$-151926856908750000$$ $$$$ $$2764800$$ $$1.9812$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 254100.by have rank $$2$$.

## Complex multiplication

The elliptic curves in class 254100.by do not have complex multiplication.

## Modular form 254100.2.a.by

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} - 6q^{13} + 2q^{17} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 