# Properties

 Label 94640.bz Number of curves $4$ Conductor $94640$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("94640.bz1")

sage: E.isogeny_class()

## Elliptic curves in class 94640.bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
94640.bz1 94640cj4 [0, 0, 0, -723827, 237016754] [2] 737280
94640.bz2 94640cj3 [0, 0, 0, -237107, -41527694] [2] 737280
94640.bz3 94640cj2 [0, 0, 0, -47827, 3255954] [2, 2] 368640
94640.bz4 94640cj1 [0, 0, 0, 6253, 303186] [2] 184320 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 94640.bz have rank $$1$$.

## Modular form 94640.2.a.bz

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.