# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 62400.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.f1 62400bi4 $$[0, -1, 0, -832033, 292395937]$$ $$31103978031362/195$$ $$399360000000$$ $$[4]$$ $$589824$$ $$1.8317$$
62400.f2 62400bi3 $$[0, -1, 0, -72033, 755937]$$ $$20183398562/11567205$$ $$23689635840000000$$ $$[2]$$ $$589824$$ $$1.8317$$
62400.f3 62400bi2 $$[0, -1, 0, -52033, 4575937]$$ $$15214885924/38025$$ $$38937600000000$$ $$[2, 2]$$ $$294912$$ $$1.4851$$
62400.f4 62400bi1 $$[0, -1, 0, -2033, 125937]$$ $$-3631696/24375$$ $$-6240000000000$$ $$[2]$$ $$147456$$ $$1.1385$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 62400.2.a.f

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 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.