# Properties

 Label 30345.j Number of curves 2 Conductor 30345 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30345.j1")

sage: E.isogeny_class()

## Elliptic curves in class 30345.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.j1 30345u2 [1, 0, 0, -60696, -2816835]  208896
30345.j2 30345u1 [1, 0, 0, 12999, -325944]  104448 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 30345.j have rank $$0$$.

## Modular form 30345.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - q^{7} + 3q^{8} + q^{9} + q^{10} + 2q^{11} - q^{12} + 2q^{13} + q^{14} - q^{15} - q^{16} - q^{18} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 