# Properties

 Label 463680.lf Number of curves $2$ Conductor $463680$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("lf1")

sage: E.isogeny_class()

## Elliptic curves in class 463680.lf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
463680.lf1 463680lf1 $$[0, 0, 0, -3132, 18576]$$ $$10536048/5635$$ $$1817210142720$$ $$$$ $$737280$$ $$1.0436$$ $$\Gamma_0(N)$$-optimal
463680.lf2 463680lf2 $$[0, 0, 0, 11988, 145584]$$ $$147704148/92575$$ $$-119416666521600$$ $$$$ $$1474560$$ $$1.3902$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 463680.2.a.lf

sage: E.q_eigenform(10)

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