# Properties

 Label 30345v Number of curves 4 Conductor 30345 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30345.i1")

sage: E.isogeny_class()

## Elliptic curves in class 30345v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.i3 30345v1 [1, 0, 0, -96821, -11603880] [2] 110592 $$\Gamma_0(N)$$-optimal
30345.i2 30345v2 [1, 0, 0, -98266, -11240029] [2, 2] 221184
30345.i4 30345v3 [1, 0, 0, 73689, -46353240] [2] 442368
30345.i1 30345v4 [1, 0, 0, -293341, 47165426] [2] 442368

## Rank

sage: E.rank()

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

## Modular form 30345.2.a.i

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.