# Properties

 Label 310464.pq Number of curves 6 Conductor 310464 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("310464.pq1")

sage: E.isogeny_class()

## Elliptic curves in class 310464.pq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
310464.pq1 310464pq5 [0, 0, 0, -127544844, 554424316432]  31457280
310464.pq2 310464pq3 [0, 0, 0, -8016204, 8560923280] [2, 2] 15728640
310464.pq3 310464pq2 [0, 0, 0, -1101324, -248633840] [2, 2] 7864320
310464.pq4 310464pq1 [0, 0, 0, -960204, -362037872]  3932160 $$\Gamma_0(N)$$-optimal
310464.pq5 310464pq6 [0, 0, 0, 874356, 26509185808]  31457280
310464.pq6 310464pq4 [0, 0, 0, 3555636, -1800332912]  15728640

## Rank

sage: E.rank()

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

## Modular form 310464.2.a.pq

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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 