# Properties

 Label 466752.b Number of curves $2$ Conductor $466752$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 466752.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
466752.b1 466752b1 $$[0, -1, 0, -5985, -124959]$$ $$90458382169/25788048$$ $$6760182054912$$ $$$$ $$1228800$$ $$1.1685$$ $$\Gamma_0(N)$$-optimal
466752.b2 466752b2 $$[0, -1, 0, 15775, -843039]$$ $$1656015369191/2114999172$$ $$-554434342944768$$ $$$$ $$2457600$$ $$1.5150$$

## Rank

sage: E.rank()

The elliptic curves in class 466752.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 466752.b do not have complex multiplication.

## Modular form 466752.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - 4 q^{5} + q^{9} - q^{11} + q^{13} + 4 q^{15} + q^{17} - 2 q^{19} + O(q^{20})$$ ## 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 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. 