# Properties

 Label 44180.c Number of curves 4 Conductor 44180 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("44180.c1")

sage: E.isogeny_class()

## Elliptic curves in class 44180.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44180.c1 44180g3 [0, 1, 0, -91305, 10586428] [2] 156492
44180.c2 44180g4 [0, 1, 0, -80260, 13254900] [2] 312984
44180.c3 44180g1 [0, 1, 0, -2945, -43280] [2] 52164 $$\Gamma_0(N)$$-optimal
44180.c4 44180g2 [0, 1, 0, 8100, -281852] [2] 104328

## Rank

sage: E.rank()

The elliptic curves in class 44180.c have rank $$0$$.

## Modular form 44180.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{5} + 2q^{7} + q^{9} - 2q^{13} - 2q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.