# Properties

 Label 44400.r Number of curves $6$ Conductor $44400$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("44400.r1")

sage: E.isogeny_class()

## Elliptic curves in class 44400.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44400.r1 44400x4 [0, -1, 0, -136402008, -613122217488] [2] 3981312
44400.r2 44400x6 [0, -1, 0, -121250008, 511696982512] [2] 7962624
44400.r3 44400x3 [0, -1, 0, -11730008, -1732777488] [2, 2] 3981312
44400.r4 44400x2 [0, -1, 0, -8530008, -9566377488] [2, 2] 1990656
44400.r5 44400x1 [0, -1, 0, -338008, -260265488] [2] 995328 $$\Gamma_0(N)$$-optimal
44400.r6 44400x5 [0, -1, 0, 46589992, -13863337488] [2] 7962624

## Rank

sage: E.rank()

The elliptic curves in class 44400.r have rank $$0$$.

## Modular form 44400.2.a.r

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.