# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("301180.a1")

sage: E.isogeny_class()

## Elliptic curves in class 301180a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
301180.a4 301180a1 [0, 1, 0, -62061, 5808160]  1866240 $$\Gamma_0(N)$$-optimal
301180.a3 301180a2 [0, 1, 0, -137356, -11118156]  3732480
301180.a2 301180a3 [0, 1, 0, -609661, -181115100]  5598720
301180.a1 301180a4 [0, 1, 0, -9720356, -11667879356]  11197440

## Rank

sage: E.rank()

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

## 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. 