# Properties

 Label 131760.u Number of curves $3$ Conductor $131760$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 131760.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
131760.u1 131760r3 $$[0, 0, 0, -1037568, -406792528]$$ $$-124110120626946048/305$$ $$-303575040$$ $$[]$$ $$777600$$ $$1.7541$$
131760.u2 131760r1 $$[0, 0, 0, -12768, -561808]$$ $$-2081462648832/28372625$$ $$-3137785344000$$ $$[]$$ $$259200$$ $$1.2048$$ $$\Gamma_0(N)$$-optimal
131760.u3 131760r2 $$[0, 0, 0, 45792, -2830032]$$ $$131716841472/119140625$$ $$-9605304000000000$$ $$[]$$ $$777600$$ $$1.7541$$

## Rank

sage: E.rank()

The elliptic curves in class 131760.u have rank $$0$$.

## Complex multiplication

The elliptic curves in class 131760.u do not have complex multiplication.

## Modular form 131760.2.a.u

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} - 3 q^{11} - 4 q^{13} - 6 q^{17} + 7 q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 