# Properties

 Label 47096.b Number of curves $2$ Conductor $47096$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 47096.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47096.b1 47096l2 $$[0, 1, 0, -33920, -2386976]$$ $$3543122/49$$ $$59691709908992$$ $$$$ $$200704$$ $$1.4490$$
47096.b2 47096l1 $$[0, 1, 0, -280, -99456]$$ $$-4/7$$ $$-4263693564928$$ $$$$ $$100352$$ $$1.1024$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 47096.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 47096.b do not have complex multiplication.

## Modular form 47096.2.a.b

sage: E.q_eigenform(10)

$$q - 2q^{3} - 4q^{5} + q^{7} + q^{9} + 8q^{15} + 2q^{17} + 2q^{19} + O(q^{20})$$ ## 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. 