# Properties

 Label 60840ca Number of curves $4$ Conductor $60840$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ca1")

sage: E.isogeny_class()

## Elliptic curves in class 60840ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60840.bb4 60840ca1 $$[0, 0, 0, -30927, -7430254]$$ $$-3631696/24375$$ $$-21956961068640000$$ $$$$ $$516096$$ $$1.8190$$ $$\Gamma_0(N)$$-optimal
60840.bb3 60840ca2 $$[0, 0, 0, -791427, -270411154]$$ $$15214885924/38025$$ $$137011437068313600$$ $$[2, 2]$$ $$1032192$$ $$2.1656$$
60840.bb2 60840ca3 $$[0, 0, 0, -1095627, -43417114]$$ $$20183398562/11567205$$ $$83357758312361994240$$ $$$$ $$2064384$$ $$2.5122$$
60840.bb1 60840ca4 $$[0, 0, 0, -12655227, -17328182794]$$ $$31103978031362/195$$ $$1405245508392960$$ $$$$ $$2064384$$ $$2.5122$$

## Rank

sage: E.rank()

The elliptic curves in class 60840ca have rank $$0$$.

## Complex multiplication

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

## Modular form 60840.2.a.ca

sage: E.q_eigenform(10)

$$q + q^{5} - 4q^{7} + 4q^{11} - 6q^{17} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 