# Properties

 Label 463680er Number of curves $2$ Conductor $463680$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("er1")

sage: E.isogeny_class()

## Elliptic curves in class 463680er

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.er1 463680er1 $$[0, 0, 0, -13548, -334672]$$ $$1439069689/579600$$ $$110763284889600$$ $$[2]$$ $$1179648$$ $$1.3928$$ $$\Gamma_0(N)$$-optimal
463680.er2 463680er2 $$[0, 0, 0, 44052, -2431312]$$ $$49471280711/41992020$$ $$-8024799990251520$$ $$[2]$$ $$2359296$$ $$1.7394$$

## Rank

sage: E.rank()

The elliptic curves in class 463680er have rank $$0$$.

## Complex multiplication

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

## Modular form 463680.2.a.er

sage: E.q_eigenform(10)

$$q - q^{5} + q^{7} - 2q^{11} - 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.