# Properties

 Label 428400nu Number of curves $6$ Conductor $428400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("428400.nu1")

sage: E.isogeny_class()

## Elliptic curves in class 428400nu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
428400.nu5 428400nu1 [0, 0, 0, -252878475, 1545867400250] [2] 94371840 $$\Gamma_0(N)$$-optimal
428400.nu4 428400nu2 [0, 0, 0, -326606475, 570962056250] [2, 2] 188743680
428400.nu6 428400nu3 [0, 0, 0, 1259697525, 4490719240250] [2] 377487360
428400.nu2 428400nu4 [0, 0, 0, -3092558475, -65742737143750] [2, 2] 377487360
428400.nu3 428400nu5 [0, 0, 0, -1053374475, -151145802247750] [2] 754974720
428400.nu1 428400nu6 [0, 0, 0, -49386974475, -4224416420839750] [2] 754974720

## Rank

sage: E.rank()

The elliptic curves in class 428400nu have rank $$1$$.

## Modular form 428400.2.a.nu

sage: E.q_eigenform(10)

$$q + q^{7} + 4q^{11} + 2q^{13} + q^{17} - 4q^{19} + O(q^{20})$$

## 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.