# Properties

 Label 96330u Number of curves $4$ Conductor $96330$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 96330u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
96330.r3 96330u1 $$[1, 1, 0, -5242, 143044]$$ $$3301293169/22800$$ $$110051245200$$ $$$$ $$147456$$ $$0.95224$$ $$\Gamma_0(N)$$-optimal
96330.r2 96330u2 $$[1, 1, 0, -8622, -68544]$$ $$14688124849/8122500$$ $$39205756102500$$ $$[2, 2]$$ $$294912$$ $$1.2988$$
96330.r4 96330u3 $$[1, 1, 0, 33628, -499494]$$ $$871257511151/527800050$$ $$-2547590031540450$$ $$$$ $$589824$$ $$1.6454$$
96330.r1 96330u4 $$[1, 1, 0, -104952, -13111626]$$ $$26487576322129/44531250$$ $$214943838281250$$ $$$$ $$589824$$ $$1.6454$$

## Rank

sage: E.rank()

The elliptic curves in class 96330u have rank $$1$$.

## Complex multiplication

The elliptic curves in class 96330u do not have complex multiplication.

## Modular form 96330.2.a.u

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - 4q^{11} - q^{12} - q^{15} + q^{16} + 2q^{17} - q^{18} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 