# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("96330.r1")

sage: E.isogeny_class()

## Elliptic curves in class 96330.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
96330.r1 96330u4 [1, 1, 0, -104952, -13111626]  589824
96330.r2 96330u2 [1, 1, 0, -8622, -68544] [2, 2] 294912
96330.r3 96330u1 [1, 1, 0, -5242, 143044]  147456 $$\Gamma_0(N)$$-optimal
96330.r4 96330u3 [1, 1, 0, 33628, -499494]  589824

## Rank

sage: E.rank()

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

## Modular form 96330.2.a.r

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 LMFDB 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 LMFDB labels. 