# Properties

 Label 30345.m Number of curves 2 Conductor 30345 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30345.m1")

sage: E.isogeny_class()

## Elliptic curves in class 30345.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.m1 30345bg2 [1, 0, 0, -10240, -382333] [2] 55296
30345.m2 30345bg1 [1, 0, 0, 385, -23208] [2] 27648 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 30345.m have rank $$1$$.

## Modular form 30345.2.a.m

sage: E.q_eigenform(10)

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

## 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 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.