# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 10304.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10304.u1 10304q2 $$[0, 0, 0, -15244, -722160]$$ $$1494447319737/5411854$$ $$1418685054976$$ $$[2]$$ $$18432$$ $$1.1927$$
10304.u2 10304q1 $$[0, 0, 0, -524, -21488]$$ $$-60698457/725788$$ $$-190260969472$$ $$[2]$$ $$9216$$ $$0.84615$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 10304.2.a.u

sage: E.q_eigenform(10)

$$q + 2q^{5} - q^{7} - 3q^{9} - 4q^{11} - 4q^{13} - 8q^{17} - 2q^{19} + O(q^{20})$$

## 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.