# Properties

 Label 9464d Number of curves $4$ Conductor $9464$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 9464d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9464.c4 9464d1 [0, 0, 0, 169, 4394] [2] 4608 $$\Gamma_0(N)$$-optimal
9464.c3 9464d2 [0, 0, 0, -3211, 65910] [2, 2] 9216
9464.c2 9464d3 [0, 0, 0, -9971, -303186] [2] 18432
9464.c1 9464d4 [0, 0, 0, -50531, 4372030] [2] 18432

## Rank

sage: E.rank()

The elliptic curves in class 9464d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9464d do not have complex multiplication.

## Modular form9464.2.a.d

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - 3q^{9} + 4q^{11} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.