# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("30345.o1")

sage: E.isogeny_class()

## Elliptic curves in class 30345.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.o1 30345i2 [0, -1, 1, -3578205, -2604036922] [] 456192
30345.o2 30345i1 [0, -1, 1, -40845, -4121539] [] 152064 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 30345.2.a.o

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 