# Properties

 Label 463680gf Number of curves $2$ Conductor $463680$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gf1")

sage: E.isogeny_class()

## Elliptic curves in class 463680gf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.gf1 463680gf1 $$[0, 0, 0, -734508, 237686832]$$ $$8493409990827/185150000$$ $$955333332172800000$$ $$[2]$$ $$5898240$$ $$2.2383$$ $$\Gamma_0(N)$$-optimal
463680.gf2 463680gf2 $$[0, 0, 0, 60372, 725107248]$$ $$4716275733/44023437500$$ $$-227151267840000000000$$ $$[2]$$ $$11796480$$ $$2.5849$$

## Rank

sage: E.rank()

The elliptic curves in class 463680gf have rank $$1$$.

## Complex multiplication

The elliptic curves in class 463680gf do not have complex multiplication.

## Modular form 463680.2.a.gf

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} + 2q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.