# Properties

 Label 10304y Number of curves $2$ Conductor $10304$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 10304y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10304.bb2 10304y1 $$[0, -1, 0, 2207, -188415]$$ $$4533086375/60669952$$ $$-15904263897088$$ $$[2]$$ $$21504$$ $$1.2139$$ $$\Gamma_0(N)$$-optimal
10304.bb1 10304y2 $$[0, -1, 0, -38753, -2736127]$$ $$24553362849625/1755162752$$ $$460105384460288$$ $$[2]$$ $$43008$$ $$1.5605$$

## Rank

sage: E.rank()

The elliptic curves in class 10304y have rank $$1$$.

## Complex multiplication

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

## Modular form 10304.2.a.y

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels.