# Properties

 Label 10304.f Number of curves $2$ Conductor $10304$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 10304.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10304.f1 10304e2 $$[0, 1, 0, -1953, 32575]$$ $$12576878500/1127$$ $$73859072$$ $$$$ $$5120$$ $$0.54982$$
10304.f2 10304e1 $$[0, 1, 0, -113, 559]$$ $$-9826000/3703$$ $$-60669952$$ $$$$ $$2560$$ $$0.20324$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 10304.f have rank $$2$$.

## Complex multiplication

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

## Modular form 10304.2.a.f

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{7} + q^{9} - 4q^{11} - 6q^{13} + O(q^{20})$$ ## 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. 