# Properties

 Label 481338t Number of curves $2$ Conductor $481338$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 481338t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
481338.t1 481338t1 $$[1, -1, 0, -3289347, -2087747051]$$ $$3047678972871625/304559880768$$ $$393329330654331120192$$ $$[2]$$ $$20643840$$ $$2.6881$$ $$\Gamma_0(N)$$-optimal
481338.t2 481338t2 $$[1, -1, 0, 4072293, -10110462323]$$ $$5783051584712375/37533175779528$$ $$-48472894294107017938632$$ $$[2]$$ $$41287680$$ $$3.0347$$

## Rank

sage: E.rank()

The elliptic curves in class 481338t have rank $$1$$.

## Complex multiplication

The elliptic curves in class 481338t do not have complex multiplication.

## Modular form 481338.2.a.t

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 2 q^{7} - q^{8} - q^{13} + 2 q^{14} + q^{16} - q^{17} - 4 q^{19} + O(q^{20})$$

## 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.