# Properties

 Label 182.c Number of curves $4$ Conductor $182$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 182.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
182.c1 182a4 [1, -1, 1, -59134, 5547693] [2] 720
182.c2 182a3 [1, -1, 1, -31294, -2081875] [2] 720
182.c3 182a2 [1, -1, 1, -4254, 59693] [2, 2] 360
182.c4 182a1 [1, -1, 1, 866, 6445] [4] 180 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form182.2.a.c

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2q^{5} - q^{7} + q^{8} - 3q^{9} + 2q^{10} + 4q^{11} - q^{13} - q^{14} + q^{16} - 6q^{17} - 3q^{18} + O(q^{20})$$

## 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.