# Properties

 Label 40362bc Number of curves $6$ Conductor $40362$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("40362.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 40362bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40362.bb5 40362bc1 [1, 0, 0, -3864, -204480] [2] 122880 $$\Gamma_0(N)$$-optimal
40362.bb4 40362bc2 [1, 0, 0, -80744, -8830416] [2, 2] 245760
40362.bb3 40362bc3 [1, 0, 0, -99964, -4313716] [2, 2] 491520
40362.bb1 40362bc4 [1, 0, 0, -1291604, -565099500] [2] 491520
40362.bb6 40362bc5 [1, 0, 0, 370926, -33226362] [2] 983040
40362.bb2 40362bc6 [1, 0, 0, -878374, 313744610] [2] 983040

## Rank

sage: E.rank()

The elliptic curves in class 40362bc have rank $$0$$.

## Modular form 40362.2.a.bb

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - 2q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - 2q^{10} + 4q^{11} + q^{12} - 6q^{13} - q^{14} - 2q^{15} + q^{16} - 2q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.