# Properties

 Label 62400bi Number of curves $4$ Conductor $62400$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bi1")

sage: E.isogeny_class()

## Elliptic curves in class 62400bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62400.f4 62400bi1 [0, -1, 0, -2033, 125937] [2] 147456 $$\Gamma_0(N)$$-optimal
62400.f3 62400bi2 [0, -1, 0, -52033, 4575937] [2, 2] 294912
62400.f2 62400bi3 [0, -1, 0, -72033, 755937] [2] 589824
62400.f1 62400bi4 [0, -1, 0, -832033, 292395937] [4] 589824

## Rank

sage: E.rank()

The elliptic curves in class 62400bi have rank $$2$$.

## Complex multiplication

The elliptic curves in class 62400bi do not have complex multiplication.

## Modular form 62400.2.a.bi

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} - 4q^{11} + q^{13} - 6q^{17} + O(q^{20})$$

## 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 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.