# Properties

 Label 29400r Number of curves $6$ Conductor $29400$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("29400.i1")

sage: E.isogeny_class()

## Elliptic curves in class 29400r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29400.i4 29400r1 [0, -1, 0, -214783, -38241188] [2] 147456 $$\Gamma_0(N)$$-optimal
29400.i3 29400r2 [0, -1, 0, -220908, -35938188] [2, 2] 294912
29400.i5 29400r3 [0, -1, 0, 293592, -178969188] [2] 589824
29400.i2 29400r4 [0, -1, 0, -833408, 254386812] [2, 2] 589824
29400.i6 29400r5 [0, -1, 0, 1371592, 1370116812] [2] 1179648
29400.i1 29400r6 [0, -1, 0, -12838408, 17709656812] [2] 1179648

## Rank

sage: E.rank()

The elliptic curves in class 29400r have rank $$0$$.

## Modular form 29400.2.a.i

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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.