# Properties

 Label 377520fk Number of curves $2$ Conductor $377520$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fk1")

sage: E.isogeny_class()

## Elliptic curves in class 377520fk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
377520.fk2 377520fk1 $$[0, 1, 0, 7704, -719820]$$ $$6967871/35100$$ $$-254696616345600$$ $$[2]$$ $$1474560$$ $$1.4465$$ $$\Gamma_0(N)$$-optimal
377520.fk1 377520fk2 $$[0, 1, 0, -89096, -9199500]$$ $$10779215329/1232010$$ $$8939851233730560$$ $$[2]$$ $$2949120$$ $$1.7931$$

## Rank

sage: E.rank()

The elliptic curves in class 377520fk have rank $$1$$.

## Complex multiplication

The elliptic curves in class 377520fk do not have complex multiplication.

## Modular form 377520.2.a.fk

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + 2q^{7} + q^{9} + q^{13} - q^{15} - 8q^{17} - 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.