# Properties

 Label 182.d Number of curves $3$ Conductor $182$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 182.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
182.d1 182b3 [1, 0, 0, -15663, -755809] [] 108
182.d2 182b2 [1, 0, 0, -193, -1055]  36
182.d3 182b1 [1, 0, 0, 7, -7]  12 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 182.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 182.d do not have complex multiplication.

## Modular form182.2.a.d

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} - 2q^{9} - 3q^{11} + q^{12} + q^{13} + q^{14} + q^{16} - 2q^{18} + 2q^{19} + O(q^{20})$$

## 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. 