# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("96330.ba1")

sage: E.isogeny_class()

## Elliptic curves in class 96330.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
96330.ba1 96330bf4 [1, 0, 1, -513764, 141697376]  884736
96330.ba2 96330bf3 [1, 0, 1, -37184, 1465232]  884736
96330.ba3 96330bf2 [1, 0, 1, -32114, 2211536] [2, 2] 442368
96330.ba4 96330bf1 [1, 0, 1, -1694, 45632]  221184 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 96330.2.a.ba

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 4q^{7} - q^{8} + q^{9} + q^{10} + 4q^{11} + q^{12} + 4q^{14} - q^{15} + q^{16} - 2q^{17} - q^{18} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 