# Properties

 Label 381150cu Number of curves $2$ Conductor $381150$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cu1")

sage: E.isogeny_class()

## Elliptic curves in class 381150cu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
381150.cu2 381150cu1 $$[1, -1, 0, 26658, -142884]$$ $$2595575/1512$$ $$-1220437230705000$$ $$[]$$ $$1866240$$ $$1.5843$$ $$\Gamma_0(N)$$-optimal
381150.cu1 381150cu2 $$[1, -1, 0, -381717, -95947659]$$ $$-7620530425/526848$$ $$-425254572832320000$$ $$[]$$ $$5598720$$ $$2.1336$$

## Rank

sage: E.rank()

The elliptic curves in class 381150cu have rank $$0$$.

## Complex multiplication

The elliptic curves in class 381150cu do not have complex multiplication.

## Modular form 381150.2.a.cu

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{7} - q^{8} + q^{13} + q^{14} + q^{16} + 3q^{17} + 4q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 