# Properties

 Label 479808.ni Number of curves $6$ Conductor $479808$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("479808.ni1")

sage: E.isogeny_class()

## Elliptic curves in class 479808.ni

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
479808.ni1 479808ni5 [0, 0, 0, -387193879884, 92734389270274192] [2] 2264924160 $$\Gamma_0(N)$$-optimal*
479808.ni2 479808ni3 [0, 0, 0, -24245658444, 1443184565779600] [2, 2] 1132462080 $$\Gamma_0(N)$$-optimal*
479808.ni3 479808ni6 [0, 0, 0, -8258455884, 3317952650942608] [2] 2264924160
479808.ni4 479808ni2 [0, 0, 0, -2560594764, -12533759058800] [2, 2] 566231040 $$\Gamma_0(N)$$-optimal*
479808.ni5 479808ni1 [0, 0, 0, -1982567244, -33934881170288] [2] 283115520 $$\Gamma_0(N)$$-optimal*
479808.ni6 479808ni4 [0, 0, 0, 9876028596, -98580268761968] [2] 1132462080
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 479808.ni5.

## Rank

sage: E.rank()

The elliptic curves in class 479808.ni have rank $$1$$.

## Modular form 479808.2.a.ni

sage: E.q_eigenform(10)

$$q + 2q^{5} - 4q^{11} - 2q^{13} + q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels.