# Properties

 Label 301180a Number of curves $4$ Conductor $301180$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 301180a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301180.a4 301180a1 $$[0, 1, 0, -62061, 5808160]$$ $$643956736/15125$$ $$620905790978000$$ $$$$ $$1866240$$ $$1.6240$$ $$\Gamma_0(N)$$-optimal
301180.a3 301180a2 $$[0, 1, 0, -137356, -11118156]$$ $$436334416/171875$$ $$112891961996000000$$ $$$$ $$3732480$$ $$1.9706$$
301180.a2 301180a3 $$[0, 1, 0, -609661, -181115100]$$ $$610462990336/8857805$$ $$363627267428355920$$ $$$$ $$5598720$$ $$2.1733$$
301180.a1 301180a4 $$[0, 1, 0, -9720356, -11667879356]$$ $$154639330142416/33275$$ $$21855883842425600$$ $$$$ $$11197440$$ $$2.5199$$

## Rank

sage: E.rank()

The elliptic curves in class 301180a have rank $$2$$.

## Complex multiplication

The elliptic curves in class 301180a do not have complex multiplication.

## Modular form 301180.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{5} - 4q^{7} + q^{9} - q^{11} + 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 