# Properties

 Label 10304.bg Number of curves $2$ Conductor $10304$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 10304.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10304.bg1 10304s2 $$[0, -1, 0, -897, 8993]$$ $$304821217/51842$$ $$13590069248$$ $$[2]$$ $$9216$$ $$0.66503$$
10304.bg2 10304s1 $$[0, -1, 0, -257, -1375]$$ $$7189057/644$$ $$168820736$$ $$[2]$$ $$4608$$ $$0.31846$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 10304.bg have rank $$0$$.

## Complex multiplication

The elliptic curves in class 10304.bg do not have complex multiplication.

## Modular form 10304.2.a.bg

sage: E.q_eigenform(10)

$$q + 2q^{3} + 2q^{5} - q^{7} + q^{9} + 6q^{11} + 4q^{13} + 4q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.