# Properties

 Label 60840.ba Number of curves $4$ Conductor $60840$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("ba1")

E.isogeny_class()

## Elliptic curves in class 60840.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60840.ba1 60840z4 $$[0, 0, 0, -854194107, 9609105685894]$$ $$19129597231400697604/26325$$ $$94854071816524800$$ $$[2]$$ $$8257536$$ $$3.4239$$
60840.ba2 60840z2 $$[0, 0, 0, -53387607, 150139469194]$$ $$18681746265374416/693005625$$ $$624258360142503840000$$ $$[2, 2]$$ $$4128768$$ $$3.0773$$
60840.ba3 60840z3 $$[0, 0, 0, -50923587, 164624457166]$$ $$-4053153720264484/903687890625$$ $$-3256162434076640400000000$$ $$[2]$$ $$8257536$$ $$3.4239$$
60840.ba4 60840z1 $$[0, 0, 0, -3491202, 2116794121]$$ $$83587439220736/13990184325$$ $$787645980941339941200$$ $$[2]$$ $$2064384$$ $$2.7307$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 60840.ba have rank $$1$$.

## Complex multiplication

The elliptic curves in class 60840.ba do not have complex multiplication.

## Modular form 60840.2.a.ba

sage: E.q_eigenform(10)

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

## 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.