# Properties

 Label 62400.l Number of curves $4$ Conductor $62400$ CM no Rank $2$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 62400.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.l1 62400bg4 $$[0, -1, 0, -30433, -1983263]$$ $$3044193988/85293$$ $$87340032000000$$ $$$$ $$262144$$ $$1.4541$$
62400.l2 62400bg2 $$[0, -1, 0, -4433, 70737]$$ $$37642192/13689$$ $$3504384000000$$ $$[2, 2]$$ $$131072$$ $$1.1076$$
62400.l3 62400bg1 $$[0, -1, 0, -3933, 96237]$$ $$420616192/117$$ $$1872000000$$ $$$$ $$65536$$ $$0.76098$$ $$\Gamma_0(N)$$-optimal
62400.l4 62400bg3 $$[0, -1, 0, 13567, 484737]$$ $$269676572/257049$$ $$-263218176000000$$ $$$$ $$262144$$ $$1.4541$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 62400.2.a.l

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} + q^{13} - 2q^{17} - 8q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 