# Properties

 Label 301530.cj Number of curves $4$ Conductor $301530$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("301530.cj1")

sage: E.isogeny_class()

## Elliptic curves in class 301530.cj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
301530.cj1 301530cj3 [1, 1, 1, -328520, 72233207]  3153920
301530.cj2 301530cj2 [1, 1, 1, -26990, 348455] [2, 2] 1576960
301530.cj3 301530cj1 [1, 1, 1, -16410, -811113]  788480 $$\Gamma_0(N)$$-optimal
301530.cj4 301530cj4 [1, 1, 1, 105260, 2887655]  3153920

## Rank

sage: E.rank()

The elliptic curves in class 301530.cj have rank $$1$$.

## Modular form 301530.2.a.cj

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + 2q^{13} - q^{15} + q^{16} - 2q^{17} + q^{18} + q^{19} + O(q^{20})$$

## 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. 