# Properties

 Label 310464nz Number of curves 6 Conductor 310464 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("310464.nz1")

sage: E.isogeny_class()

## Elliptic curves in class 310464nz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
310464.nz4 310464nz1 [0, 0, 0, -960204, 362037872] [2] 3932160 $$\Gamma_0(N)$$-optimal
310464.nz3 310464nz2 [0, 0, 0, -1101324, 248633840] [2, 2] 7864320
310464.nz6 310464nz3 [0, 0, 0, 3555636, 1800332912] [2] 15728640
310464.nz2 310464nz4 [0, 0, 0, -8016204, -8560923280] [2, 2] 15728640
310464.nz5 310464nz5 [0, 0, 0, 874356, -26509185808] [2] 31457280
310464.nz1 310464nz6 [0, 0, 0, -127544844, -554424316432] [2] 31457280

## Rank

sage: E.rank()

The elliptic curves in class 310464nz have rank $$1$$.

## Modular form 310464.2.a.nz

sage: E.q_eigenform(10)

$$q + 2q^{5} - q^{11} + 6q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.